Question

A ball is thrown from a hot air balloon that is at rest 245 m above the ground. How long will it take for the ball to reach the ground? How fast will the ball be traveling when it reaches the ground?

Answer 1

Answer:

7.07 s

69.3 m/s

Explanation:

Taking the negative direction to be down and the positive direction to be up:

We have 3 variables in the y-direction and can solve for time.

• v₀ = 0 m/s
• a = -9/8 m/s²
• Δy = -245 m
• t = ?

Use this kinematics equation to solve for time.

• Δx = v₀t + 1/2at²

• -245 = 1/2(-9.8)t²
• -245 = -4.9t²
• t² = 50
• t = 7.07106781187

It will take the ball 7.07 s to reach the ground.

We can solve for final velocity using the same variables in the y-direction:

• v₀ = 0 m/s
• a = -9/8 m/s²
• Δy = -245 m  
• v = ?

Use this kinematics equation to solve for final velocity.

• v² = v₀² + 2aΔx
• v² = 2(-9.8)(-245)
• v² = 4802
• v = 69.2964645563

The ball will be traveling at a speed of 69.3 m/s at the instant before it reaches the ground.