Question

Anna is sitting in a moving cart and throws a ball straight up. Theoretically, the ball should land in the cart, but it lands on the ground a little before the cart. What is the reason for the difference in the ranges of the ball and the cart?

Answer 1

Answer:

Reason for the difference in the ranges of the ball and the cart:

"the average speed of the cart is less than the instant speed of the cart at the time of throwing the ball".

Explanation:

Assuming that the air friction is negligible.

Given that the ball lands on the ground a little before the cart.

So, the range of the ball is more than the range of the cart in the same time interval.

Let the instant speed of the cart is v m/s  at the time of throwing the ball in the vertically upward direction, so the speed of the ball in the horizontal direction = v m/s.

Let t be the total time of flight of the ball.

As the gravitational force is acting in the downward direction so it will not change the horizontal velocity of the ball.

So, the range covered by the ball $= vt$ m.

Let u be the average speed of the cart for the time t s (same as the time of flight of ball).

So, the distance by the cart $= ut$ m

As the range of the ball is more than the range of the cart in the same time interval, so

$vt > ut \\\\\Rightarrow v>u.$

So, the reason for the difference in the ranges of the ball and the cart is "the average speed of the cart is less than the instant speed of the cart at the time of throwing the ball".