A red ball and a green ball are simultaneously thrown horizontally from the same height. The red ball has an initial speed of 40 m/s and the green ball has an initial speed of 20 m/s. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground will be

The time taken by the green ball to reach ground will be twice the time taken by the red ball.

Given data:

The initial velocity of red ball is, u = 40 m/s.

The initial velocity of green ball is, u' = 20 m/s.

In this problem when each ball reaches the ground, they will come to rest. Hence, the final velocity of each ball will be zero. So, in this sense we can use the first kinematic equation of motion as,

For red ball,

v = u + (-g)t

0 = 40 - (9.8)t

t = 40/9.8

t = 4.08 s

Now, for green ball,

v = u' + (-g)t'

0 = 20 - 9.8t'

t' = 20/9.8

t' = 2.04 s

Clearly,

t' = 2t

Thus, we can conclude that the time taken by the green ball to reach ground will be twice the time taken by the red ball.

Learn more about the kinematic equations of motion here:

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The green ball will get to the ground first because the time taken for the green ball to get to the ground is small when compared to that of the red ball.

Explanation:

From the question given above, the following data were obtained:

For the Red ball:

Initial velocity (u) = 40 m/s

For the Green ball:

Initial velocity (u) = 20 m/s.

Next, we shall determine the time taken for each ball to get to its maximum height.

For the Red ball:

Initial velocity (u) = 40 m/s

Acceleration due to gravity (g) = 9.8 m/s²

Final velocity (v) = 0 m/s (at maximum height)

Time (t) to reach the maximum height =?

v = u – gt (since the ball is going against gravity)

0 = 40 – 9.8t

Rearrange

9.8t = 40

Divide both side by 9.8

t = 40/9.8

t = 4.08 s

For the Green ball:

Initial velocity (u) = 20 m/s.

Acceleration due to gravity (g) = 9.8 m/s²

Final velocity (v) = 0 m/s (at maximum height)

Time (t) to reach the maximum height =?

v = u – gt (since the ball is going against gravity)

0 = 20 – 9.8t

Rearrange

9.8t = 20

Divide both side by 9.8

t= 20/9.8

t = 2.04 s

Finally, we shall determine the time taken for each ball to reach the ground.

For Red ball:

Time (t) to reach maximum height = 4.08 s

Time (T) to reach the ground =?

T = 2t

T = 2 × 4.08

T = 8.16 s

For Green ball:

Time (t) to reach maximum height = 2.04 s

Time (T) to reach the ground =?

T = 2t

T = 2 × 2.04

T = 4.08 s

Summary:

Ball >>>>>> Time to reach the ground

Red >>>>>> 8.16 s

Green >>>> 4.08 s

From the above illustration, we can see that the green ball will get to the ground first because the time taken for the green ball to get to the ground is small when compared to that of the red ball.