Question

A truck of height 10 m and length 20 m is moving with a constant velocity of v = 5 m/sec. A ball, 30 m away from the truck, is projected with a velocity of $20$ m/sec at an angle 37${}^o$ with horizontal. At how much distance from point A (top corner of the truck), will the ball strike the truck ?

• A. 2.86 m
• B. 7.14 m
• C. 3.86 m
• D. none of these

Answer 1

The correct option is A 2.86 m

If $s_1$ and $s_2$ are the distances covered by the ball and the truck respectively, then we can calculate the time after which they collide using
$s_1+s_2=30$
or
$20cos{37}^{o}t+5t=30$ (using $s=ut$)
or
$t=\frac{30}{21}=1.43s$
Now in this time the displacement of the ball in y direction is given as
$s_y=vsin{37}^{o}t-\frac{1}{2}g{t}^2$
$=20\times 0.6\times 1.43-\frac{1}{2}\times 9.8\times {1.43}^2$
$=7.14m$
Thus from point A the ball will be at $10-7.14=2.86m$