Question

A soccer ball is kicked straight upwards with an initial vertical speed of 8.0 m/s. We can ignore air resistance. How long does it take the ball to have a downwards speed of 4.0 m/s?

Answer 1

Answer:

The time the ball it takes to have the downward speed 4 m/s is 1.22 sec.

Explanation:

Lets explain the motion of the ball

The ball is kicked straight upwards with an initial vertical speed of 8.0 m/s

Its velocity decreases util it reaches the maximum height

At the maximum height its velocity is equal to zero

Then it fall down to the ground

We can ignore air resistance

Lets find the time it takes the ball to reach the maximum height

The acceleration of gravity is -9.8 m/s²

The initial velocity is 8 m/s upward

The final velocity is zero

So lets use the rule v = u + gt, where v is the final velocity, u is the initial

velocity, g is the acceleration of gravity and t is the time

u = 8 , v = 0 , g = -9.8

Substitute these value in the equation above

0 = 8 - 9.8 t

Add 9.8 t for both sides

9.8 t = 8

Divide both sides by 9.8

t = 40/49 seconds

The ball falls withe initial velocity zero and increases to reach 4 m/s

The velocity 4 m/s is downward

The acceleration of gravity is 9.8 m/s²

By using the same rule

u = 0 , v = 4 , g = 9.8

4 = 0 + 9.8 t

4 = 9.8 t

Divide both sides by 9.8

t = 20/49

The time the ball it takes to have the downward speed 4 m/s is the sum

of the two times above

The time the ball it takes = $\frac{40}{49}+\frac{20}{49}=\frac{60}{49}=1.22$ seconds

The time the ball it takes to have the downward speed 4 m/s is 1.22 sec.