Question

For a car that can go from 0 to 60 mph in 4 seconds: 8 seconds after being launched, what is the height of a ball that starts from a height of 12 m with an initial upward velocity of 24 m/s?

Answer 1

The question involves calculating the height of a ball after 8 seconds given its initial conditions using the equation of motion under gravity. The calculated result suggests an error with the time or the application of physics. A further check shows the time to reach the ball's maximum height is less than 8 seconds.

The question involves calculating the height of a ball after 8 seconds given its initial conditions using the equation of motion under gravity. The calculated result suggests an error with the time or the application of physics. A further check shows the time to reach the ball's maximum height is less than 8 seconds.

Step-by-step explanation:

The student asked what is the height of a ball that starts from a height of 12 m with an initial upward velocity of 24 m/s after 8 seconds. To solve this, we can use the equation of motion for an object under gravity:

Equation of motion:

h = h0 + v0t - ½gt²

where:

h is the final height,

h0 is the initial height (12 m),

v0 is the initial velocity (24 m/s),

t is the time (8 s),

g is the acceleration due to gravity (9.81 m/s²).

By substituting the known values:

h = 12 m + (24 m/s)(8 s) - ½(9.81 m/s²)(8 s)²

h = 12 m + 192 m - 313.92 m

h = -109.92 m

However, this result would suggest that the ball is below the starting point, which isn't possible after only 8 seconds, since the ball would initially be going up due to its initial upward velocity. This indicates an error in our calculation or understanding of the physical scenario. The time given might be too long, or the question might be incorrectly asking for a time when the ball is in fact on its way down after reaching its apex. Therefore, we would need to first calculate the time for the ball to reach its maximum height, and then determine its behavior after that point.

Considering the time to reach maximum height:

tmax = v0 / g

tmax = 24 m/s / 9.81 m/s²

tmax ≈ 2.45 s

This is less than the 8 seconds given, confirming that the given time is beyond the point at which the ball would have started descending.