Calculating the Time for a Ball to Strike the Ground

Calculation Process

If a ball is thrown straight upwards at a speed of 11 m/s from a balcony 4 m above the ground, how much time would it take to strike the ground at the base of the balcony?

The time it takes for the ball to strike the ground at the base of the balcony is 1.24 seconds. This equation can be rearranged to form a quadratic equation, which can be solved to find the values of t. In this case, the solution is t = 1.24 seconds.

Explanation

To find the time it takes for the ball to strike the ground, we can use the equation for vertical motion: h = ut + (1/2)gt^2, where:
- h is the height
- u is the initial velocity
- g is the acceleration due to gravity
- t is the time

Since the ball is thrown upwards, the initial velocity u is positive. By substituting the known values, we have 4 = 11t - (1/2)(9.8)t^2. This equation can be rearranged to form a quadratic equation, which can be solved to find the values of t. In this case, the solution is t = 1.24 seconds.