A boy throws a ball in air at $60^{\circ}$ to the horizontal along a road with a speed of $10 m / s (36 k m / h)$ . Another boy sitting in a passing by car observes the ball. Sketch the motion of the ball as observed by the boy in the car, if car has a speed of $(18 k m / h)$ . Give explanation to support your diagram.

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Solution

Step 1 : Motion of ball with respect to boy
$u_{B} = 5^i + 5 \sqrt{3}^j$

This is simply a projectile motion.

Step 2: Motion of a ball with respect to moving car
As car is also moving with a constant speed of $18 k m / h$
$u_{C} = 18 k m / h = 18 \times \frac{5}{18} = 5 m / s$
${\to u}_{B C} = {\to u}_{B} - {\to u}_{C}$
${\to u}_{B C} = (5^i + 5 \sqrt{3}^j) - 5^i$
${\to u}_{B C} = 5 \sqrt{3}^j$

This diagram indicates that boy sitting in the car observes the ball on its overhead as both car and ball are moving with same horizontal speed.

So, boy sitting in the car observes the ball in vertical upward direction.

Final answer:

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A boy throws a ball in air at 60∘ to the horizontal along a road with a speed of 10m/s (36 km/h). Another boy sitting in a passing by car observes the ball. Sketch the motion of the ball as observed by the boy in the car, if car has a speed of (18 km/h). Give explanation to support your diagram.