The problem involves two stages:

1. The ball is moving with the balloon: Since the ball is gently released from the balloon, it initially has the same velocity as the balloon, which is 4 m/s.

2. The ball is falling under gravity: After being released, the ball is under the influence of gravity alone.

We know that the total time for the ball to hit the ground is 4 seconds.

Let's denote the time the ball spends moving with the balloon as t1 and the time it spends falling under gravity as t2. We know that t1 + t2 = 4 seconds.

We can find t1 by using the equation of motion: h = ut + 0.5gt^2, where u is the initial velocity, g is the acceleration due to gravity, and t is the time.

For the first stage, h = 4t1 (since the initial velocity u = 4 m/s and there's no acceleration as the ball is moving with constant velocity).

For the second stage, h = 0.5*9.8*t2^2 (since the initial velocity u = 0 and the acceleration g = 9.8 m/s^2).

Adding these two equations together gives the total height h:

h = 4t1 + 0.5*9.8*t2^2.

We also know that t1 + t2 = 4, so we can substitute t2 = 4 - t1 into the equation for h:

h = 4t1 + 0.5*9.8*(4 - t1)^2.

This is a quadratic equation in t1, which we can solve to find the time t1 that the ball spends moving with the balloon. Once we have t1, we can substitute it back into the equation h = 4t1 to find the height h.

Question

The problem involves two stages:

1. The ball is moving with the balloon: Since the ball is gently released from the balloon, it initially has the same velocity as the balloon, which is 4 m/s.

2. The ball is falling under gravity: After being released, the ball is under the influence of gravity alone.

We know that the total time for the ball to hit the ground is 4 seconds.

Let's denote the time the ball spends moving with the balloon as t1 and the time it spends falling under gravity as t2. We know that t1 + t2 = 4 seconds.

We can find t1 by using the equation of motion: h = ut + 0.5gt^2, where u is the initial velocity, g is the acceleration due to gravity, and t is the time.

For the first stage, h = 4t1 (since the initial velocity u = 4 m/s and there's no acceleration as the ball is moving with constant velocity).

For the second stage, h = 0.5*9.8*t2^2 (since the initial velocity u = 0 and the acceleration g = 9.8 m/s^2).

Adding these two equations together gives the total height h:

h = 4t1 + 0.5*9.8*t2^2.

We also know that t1 + t2 = 4, so we can substitute t2 = 4 - t1 into the equation for h:

h = 4t1 + 0.5*9.8*(4 - t1)^2.

This is a quadratic equation in t1, which we can solve to find the time t1 that the ball spends moving with the balloon. Once we have t1, we can substitute it back into the equation h = 4t1 to find the height h.

Knowee AI · Accepted Answer