Question

Tad drops a cherry pit out the car window 1. 0 m above the

ground while traveling down the road at 18 m/s. How far,


horizontally, from the initial dropping point will the pit hit the


ground?

Answer 1

To calculate the distance the cherry pit will travel horizontally, we use the time it takes for the pit to fall vertically to the ground, then multiply that time by the car's horizontal velocity. The cherry pit travels horizontally for about 8.12 meters before it hits the ground.

Step-by-step explanation:

Calculating Horizontal Displacement

To determine how far horizontally the cherry pit will travel before hitting the ground, we must calculate the time it takes to reach the ground and then use the horizontal velocity to find the displacement. Since the vertical and horizontal motions are independent, we can solve for the time the cherry pit is in the air using the following formula for the vertical motion under gravity:

h = ½gt², where h is the height (1.0 m), g is the acceleration due to gravity (9.81 m/s²), and t is the time in seconds. Rearranging the formula to solve for time (t), we get t = √(2h/g).

After calculating the time, we multiply it by the horizontal velocity of the car (18 m/s) to find the horizontal displacement (x = vt).

Let's perform the calculation:

• First, find the time to hit the ground: t = √(2h/g) = √(2*1.0 m / 9.81 m/s²) = √(0.204 s²) = 0.451 s (approximately).
• Next, calculate the horizontal displacement: x = vt = 18 m/s * 0.451 s = 8.12 m.

Therefore, the cherry pit will hit the ground approximately 8.12 meters horizontally from the initial dropping point.

Answer 2

The cherry pit will hit the ground approximately 125 m horizontally from the initial dropping point.

Step-by-step explanation:

Given that the cherry pit is dropped from a height of 1.0 m and traveling at a horizontal velocity of 18 m/s, we can find the horizontal distance the pit will travel before hitting the ground.

In horizontal motion, the velocity remains constant, so the horizontal distance is given by the formula:

Distance = Velocity * Time

The time it takes for the pit to hit the ground can be determined using the equation for free fall:

h = 0.5 * g * t^2

By substituting the known values, we can solve for time, which is then used to calculate the horizontal distance traveled.

Therefore, the pit will hit the ground approximately 125 m horizontally from the initial dropping point.