Question

A car driving down Oceanside Blvd at 20m/s loses a hubcap. The hubcap travels a distance of 5 m horizontally before it hits the ground. How high above the ground was the hubcap initially?

Answer 1

To find the initial height of a hubcap falling off a moving car, we calculate the time it takes to travel horizontally before it hits the ground. Using this time in the gravitational acceleration formula, we determine that the hubcap was 0.30625 m above the ground when it fell.

Step-by-step explanation:

The question asks to determine the initial height from which a hubcap fell off a car moving at 20 m/s, given that it traveled horizontally 5m before hitting the ground. The concept we will use to solve this is the physics of projectile motion. Assuming no air resistance and using Earth's gravitational acceleration (9.81 m/s2), the vertical and horizontal motions can be analyzed independently.

To find the time to hit the ground, we consider the horizontal motion. Since the horizontal velocity is constant at 20 m/s, we can divide the horizontal distance by the horizontal velocity to find the time:

time = distance / velocity = 5m / 20 m/s = 0.25s.

This time is the same for the vertical motion. Now, using the formula h = 1/2 * g * t2, where h is height, g is gravitational acceleration, and t is time, we determine the initial height h:

h = 1/2 * 9.81 m/s2 * (0.25 s)2 = 0.30625 m.

So, the hubcap was initially 0.30625 m above the ground. Note that the horizontal motion does not affect the vertical motion, and we only consider the effect of gravity on the falling hubcap.