Final answer:
The ball will take approximately 3.77 seconds to reach its highest point, which is at a height of approximately 81.7 meters. It will take approximately 7.54 seconds to return to its original height. When the ball reaches the ground, it will have a speed of approximately 40.14 m/s.
Step-by-step explanation:
To determine the answers to the given questions, we can use the equations of motion for objects in free fall. Since the ball is thrown upwards, its initial vertical velocity is positive. We can use the equation v = u + at to find the time taken to reach the highest point. Setting the final velocity v to zero, we have 0 = 37 + (-9.8)t, where g = -9.8 m/s² is the acceleration due to gravity. Solving for t gives t ≈ 3.77 seconds.
The maximum height of the ball can be found using the equation h = ut + (1/2)gt², where h is the maximum height. Plugging in the values, h = 37 * 3.77 + (1/2) * (-9.8) * (3.77)² ≈ 81.7 meters.
The time taken to return to the original height can be found using the equation v = u + at. Since the initial velocity is 37 m/s and the acceleration is -9.8 m/s², we can set v = 0 and solve for t. The value of t will be the time taken to return to the original height. Plugging in the values, 0 = 37 + (-9.8)t. Solving for t gives t ≈ 7.54 seconds.
To determine the speed of the ball when it reaches the ground, we can use the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. Since the ball is thrown upwards, the final velocity v is negative. Plugging in the values, v² = 0² + 2 * (-9.8) * -81.7 ≈ 1611.64. Taking the square root of both sides gives v ≈ 40.14 m/s.