Question

A man standing on a truck which moves with a constant horizontal accelaration 10m/s² when the speed of the truck is 10m/s. The man throws a ball with velocity 5√2m/s with respect to truck. In the direction shown in diagram. Find the displacement of ball in metres in one second as observed by the man.(g=10m/s²)

Answer 1

speed of the truck is 10m/s

velocity of ball with respect to truck is 5√2 m/s.

Let's write it in vector form,

velocity of truck, $v_t=10\hat{i}$

velocity of ball with respect to truck, $v_{(b,t)}=v_b-v_t$

or, $5\sqrt{2}(cos45^{\circ}\hat{i}+sin45^{\circ}\hat{j})=v_b-10\hat{i}$

or, $v_b=5\hat{i}+5\hat{j}+10\hat{i}$

or, $v_b=15\hat{i}+5\hat{j}$

given, acceleration of truck with respect to ground , $a=10\hat{i}+(-g)\hat{j}$

or, $a=10\hat{i}-10\hat{j}$

now, displacement of ball with with respect to ground is $s=v_bt+\frac{1}{2}at^2$

$=(15\hat{i}+5\hat{j}).1+\frac{1}{2}(10\hat{i}-10\hat{j}).1^2$

$=20\hat{i}$

hence, displacement of ball with respect to ground is 20m

Answer 2

Answer:

20m is the right Answer

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