Question

A ball is thrown upward with a speed of 38.0 m/s from the top of a building 240 m tall.a) How long will it take for this ball to reach the ground?b) How long will it take for this ball to reach the highest point?

Answer 1

Answer:

A) The total time it takes for the ball to reach the ground = 11.702 seconds

B) The time taken by the ball to reach the highest point = 3.8 seconds

Explanations:

To get the distance from the top of the building to the maximum height reached by the ball:

`v^2=u^2\text{ + 2gh}`

The initial speed, u = 38 m/s

The final speed at the maximum height, v = 0m/s

g = -10m/s² (Since the ball is thrown upwards)

`\begin{gathered} 0^2=38^2+2(-10)h \\ 20h\text{ = }1444 \\ h\text{ = }(1444)/(20) \\ h\text{ = }72.2\text{ m} \end{gathered}`

The distance from the top of the building to the maximum height = 72.2 m

The time taken for the ball to reach the highest point from the top of the building will be calculated using the equation:

v = u + gt

0 = 38 + (-10)t

10t = 38

t = 38/10

t = 3.8 s

From the maximum height of the ball to the ground:

The height, H = 72.2 + 240

H = 312.2 m

The initial velocity, u = 0 m/s

g = 10 m/s²

Using the equation below:

`\begin{gathered} v^2=u^2+2gH \\ v^2=0^2\text{ + 2(10)}(312.2) \\ v^2\text{ = }6244 \\ v\text{ = }\sqrt[]{6244} \\ v\text{ = }79.02\text{ m/s} \end{gathered}`

The time spent from the top of the building to the the ground will be calculated using the formula:

v = u + gt

79.02 = 0 + 10t

10t = 79.02

t = 79.02/10

t = 7.902 s

The total time it takes for the ball to reach the ground = 7.902 + 3.8

The total time it takes for the ball to reach the ground = 11.702 seconds

The time taken by the ball to reach the highest point = 3.8 seconds