An NCC parade is going at a uniform speed of
Question: An NCC parade is going at a uniform speed of $6 \mathrm{~km} / \mathrm{h}$ through a place under a berry tree on which a bird is sitting at a height of $12.1 \mathrm{~m}$. A particular instant the bird drops a berry. Which cadet (give the distance from the tree at the instant) will receive the berry on his uniform? Solution: For berry, $u=0 ; a=g ; s=12.1 m$ $\mathrm{s}=\mathrm{ut+}{ }^{\frac{1}{2}} a \mathrm{t}^{2}$ $12.1=0+\frac{1}{2}(g) t^{2}$ $\mathrm{t}=1.57 \mathrm{sec}$ Distance...
Read More →Solve this following
Question: If $A(-2,0), B(0,4)$ and $C(0, k)$ be three points such that area of a $A B C$ is 4 sq units, find the value of $k$. Solution:...
Read More →A healthy young man standing at a distance of
Question: A healthy young man standing at a distance of $7 \mathrm{~m}$ from a $11: 8 \mathrm{~m}$ high building sees a kid slipping from the top floor. With what speed (assumed uniform) should he run to catch the kid at the arms height $(1.8 \mathrm{~m})$ ? Solution: For kid, $\mathrm{u}=0 ; \mathrm{a}=\mathrm{g} ; \mathrm{s}=11.8-1.8$ $\mathrm{s}=10 \mathrm{~m}$ $s=u t+\frac{1}{2} a t^{2}$ $10=0+\frac{1}{2}(g) t^{2}$ $t=1.42 \mathrm{sec}$ In this time, man has to reach building Speed= $\frac{\...
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Question: Find the value of $k$ for which the area of aABC having vertices $A(2,-6), B(5,4)$ and $C(k, 4)$ is 35 sq units. Solution:...
Read More →A person sitting on top of a tall building is dropping balls
Question: A person sitting on top of a tall building is dropping balls at regular intervals of one second. Find the positions of the $3^{\text {rd }}, 4^{\text {th }}$ and $5^{\text {th }}$ ball when the $6^{\text {th }}$ ball is being dropped. Solution: For every ball; $u=0$ and $a=g$ When $6^{\text {th }}$ ball is dropped, $5^{\text {th }}$ ball moves for 1 second, $4^{\text {th }}$ ball moves for 2 seconds, $3^{\text {rd }}$ ball moves for 3 seconds Position $S=u t+{ }^{\frac{1}{2}} a t^{2}$ ...
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Question: Find the value of $k$ for which thepoints $A(1,-1), B(2, k)$ and $C(4,5)$ are collinear. Solution:...
Read More →A stone is thrown vertically upward with a speed of
Question: A stone is thrown vertically upward with a speed of $28 \mathrm{~m} / \mathrm{s}$. (a) Find the maximum height reached by the stone. (b) Find its velocity one second before it reaches the maximum height. (c) Does the answer pf part (b) change if the initial speed is more than $28 \mathrm{~m} / \mathrm{s}$ such as $40 \mathrm{~m} / \mathrm{s}$ or 80 $\mathrm{m} / \mathrm{s}$ ? Solution: (a) $u=28 \mathrm{~m} / \mathrm{s} ; \mathrm{v}=0 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-\mathrm{g}$ ...
Read More →Find the value of
Question: Find the value of $k$ for which thepoints $P(5,5), Q(k, 1)$ and $R(11,7)$ are collinear. Solution:...
Read More →Solve this following
Question: Find the value of $k$ for which thepoints $A(3,-2), B(k, 2)$ and $C(8,8)$ are collinear. Solution:...
Read More →A ball is dropped from a balloon going up at a speed
Question: A ball is dropped from a balloon going up at a speed of $7 \mathrm{~m} / \mathrm{s}$. if the balloon was at a height $60 \mathrm{~m}$ at the time of dropping the ball, how long will the ball take in reaching the ground? Solution: $\mathrm{u}=7 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-\mathrm{g} ; \mathrm{s}=-60$ $\mathrm{s}=u t^{\frac{1}{2}} a t^{2}$ $-60=7 t^{\frac{1}{2}}(g) t^{2}$ $\mathrm{t}=4.28 \mathrm{sec}$...
Read More →Use determinants to show that the following points are collinear.
Question: Use determinants to show that the following points are collinear. $P(-2,5), Q(-6,-7)$ and $R(-5,-4)$ Solution:...
Read More →A ball is projected vertically upward with a speed of
Question: A ball is projected vertically upward with a speed of $50 \mathrm{~m} / \mathrm{s}$ Find (a) The maximum height (b) The time to reach the maximum height (c) The specd at half the maximum height. Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ Solution: $\mathrm{u}=50 \mathrm{~m} / \mathrm{s} ; \mathrm{v}=0 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-\mathrm{g}$ (a) $\mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}$ $0^{2}=(50)^{2}+2(\mathrm{~g}) \mathrm{s}$ $s=125 m$ (b) $v=u+a t$ $0=50$-gt $\...
Read More →Use determinants to show that the following points are collinear.
Question: Use determinants to show that the following points are collinear. $A(3,8), B(-4,2)$ and $C(10,14)$ Solution:...
Read More →A car travelling at
Question: A car travelling at $60 \mathrm{~km} / \mathrm{h}$ overtakes another car travelling at $42 \mathrm{~km} / \mathrm{h}$. Assuming each car to be $5.0 \mathrm{~m}$ long, find the time taken during the overtake and the total road distance used for the overtake. Solution: $\overrightarrow{\mathrm{V}}_{1}=60 \times \frac{5}{18}=16.6 \mathrm{~m} / \mathrm{s}$ $\overrightarrow{\mathrm{V}}_{2}=42 \times \frac{5}{18}=11.6 \mathrm{~m} / \mathrm{s}$ Relative velocity $=16.6-11.6$ $\mathrm{V}_{\tex...
Read More →Use determinants to show that the following points are collinear.
Question: Use determinants to show that the following points are collinear. $A(2,3), B(-1,-2)$ and $C(5,8)$ Solution:...
Read More →A police jeep is chasing a culprit going on a motorbike.
Question: A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of $72 \mathrm{~km} / \mathrm{h}$. The jeep follows it at a speed of $90 \mathrm{~km} / \mathrm{h}$, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike? Solution: $V_{\text {bike }}=72^{\times \frac{5}{18}}=20 \mathrm{~m} / \mathrm{s}$ $V_{\text {police }}=90^{\times \frac{5}{18...
Read More →Find the area of the triangle whose vertices are:
Question: Find the area of the triangle whose vertices are: $P(1,1), Q(2,7)$ and $R(10,8)$ Solution:...
Read More →Find the area of the triangle whose vertices are:
Question: Find the area of the triangle whose vertices are: $P(0,0), Q(6,0)$ and $R(4,3)$ Solution:...
Read More →Complete the following table:
Question: Complete the following table: Solution: If initial velocity is $\mathrm{u}$ and deacceleration is $-\mathrm{a}$ then braking distance $v^{2}=u^{2}+2 a s$ $0^{2}=u^{2}-2 a S$ $\mathrm{S}_{\mathrm{b}}=\frac{\mathrm{u} 2}{2 \mathrm{a}}$ (Braking distance) $\mathrm{S}_{\mathrm{R}}=\mathrm{u} \times \mathrm{t}_{\mathrm{R}}$ (Reaction distance) Total distance $=\mathrm{S}_{\mathrm{b}}+\mathrm{S}_{\mathrm{R}}$ Solve table with given values and above formulas...
Read More →Find the area of the triangle whose vertices are:
Question: Find the area of the triangle whose vertices are: $A(-8,-2), B(-4,-6)$ and $C(-1,5)$ Solution:...
Read More →A driver takes 0.20 s to apply the brakes after he sees a need for it,
Question: A driver takes $0.20$ s to apply the brakes after he sees a need for it, This is called the reaction time of the driver. If he is driving a car at a speed of $54 \mathrm{~km} / \mathrm{h}$ and the brakes cause a deceleration of $6.0 \mathrm{~m} / \mathrm{s}^{2}$, find the distance travelled by the car after he sees the need to put the brakes on. Solution: Speed of car $=54 \times \frac{5}{18}=15 \mathrm{~m} / \mathrm{s}$ Distance travelled during reaction time $\mathrm{S}_{1}=\mathrm{v...
Read More →Find the area of the triangle whose vertices are:
Question: Find the area of the triangle whose vertices are: $A(-2,4), B(2,-6)$ and $C(5,4)$ Solution:...
Read More →A particle starting from rest moves with constant acceleration.
Question: A particle starting from rest moves with constant acceleration. If it takes $5.0$ s to reach the speed $18.0$ $\mathrm{km} / \mathrm{h}$ Find (a) The average velocity during this period (b) The distance travelled by the particle during this period. Solution: $\mathrm{u}=0 ; \mathrm{t}=5 \mathrm{sec} ; \mathrm{v}=18 \times 5 / 18=5 \mathrm{~m} / \mathrm{s}$ $\mathrm{v}=\mathrm{u}+\mathrm{at}$ $5=0+a(5)$ $a=1 \mathrm{~m} / \mathrm{s}^{2}$ $S=u t^{\frac{1}{2}} a t^{2}$ $\mathrm{S}=0+\frac...
Read More →Find the area of the triangle whose vertices are:
Question: Find the area of the triangle whose vertices are: $A(3,8), B(-4,2)$ and $C(5,-1)$ Solution:...
Read More →A bullet going with speed
Question: A bullet going with speed $350 \mathrm{~m} / \mathrm{s}$ enters a concrete wall and penetrates a distance $5.0 \mathrm{~cm}$ before coming to rest. Find the deceleration. Solution: $\mathrm{u}=350 \mathrm{~m} / \mathrm{s} ; \mathrm{v}=0 ; \mathrm{s}=5 \times 10^{-2} \mathrm{~m}$ $\mathrm{v}^{2}=2^{2}+2 \mathrm{as}$ $0^{2}=(350)^{2}+2(\mathrm{a})(0.05)$ $\mathrm{a}=-12.25 \times 10^{5} \mathrm{~m} / \mathrm{s}^{2}$...
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