The player hits the ball, it's 7 feet above the ground.
This scenario sounds like it involves some good old projectile motion! To find the initial height of the ball when the player hits it, we can use some basic physics equations.
We'll use the formula for the horizontal distance traveled by a projectile:
Horizontal distance=Initial horizontal velocity×Time
And for the vertical motion, we'll use the formula:
Vertical displacement=Initial vertical velocity×Time+ 1/2 ×acceleration due to gravity×Time^2
Given:
The ball lands 15 feet away from the base of the net (horizontal distance).
The volleyball net is 8 feet tall.
We want to find the height of the ball when the player hits it.
Let's assume there's no initial vertical velocity when the player hits the ball, so the only motion affecting the vertical direction is due to gravity (assuming standard Earth gravity of 32ft/s^2 ).
The horizontal distance traveled by the ball is 15 feet, and this distance is a result of both the horizontal and vertical motion of the ball. We can use this information to solve for time.
Let's consider the horizontal and vertical components of motion separately:
Horizontal motion: There's no acceleration in the horizontal direction, so the only formula we'll use is the one that relates velocity, distance, and time:
Horizontal distance=Initial horizontal velocity×Time
Given that the ball travels 15 feet horizontally, and there's no initial horizontal velocity given, we'll assume it's constant:
Initial horizontal velocity= Horizontal distance/ Time
Vertical motion: Using the vertical motion equation and considering that the ball lands 8 feet above the ground (height of the net):
Vertical displacement= 1/ 2 ×acceleration due to gravity×Time^2
Now, let's combine these equations to solve for the time it takes for the ball to travel:
From the horizontal motion equation:
Initial horizontal velocity= 15feet/ Time
And from the vertical motion equation:
8feet= 1/ 2 ×32ft/s^2 ×Time^2
Solving the vertical motion equation for time:
Time= √2×8feet/ 32ft/s^2
Let's calculate the time it takes for the ball to reach the net and then find the initial height from the horizontal motion equation using this time.
Actually, there might be an easier way to approach this problem without getting into the specifics of time and motion equations.
Let's consider the situation at the moment the player hits the ball. The ball eventually lands 15 feet away from the net and the net is 8 feet tall.
When the player hits the ball, it's in the air and has a horizontal distance of 15 feet to cover before landing. The ball's initial vertical height plus the net's height would give us the total height at the moment of hitting.
So, the initial vertical height of the ball = Total height - Net's height.
Initial vertical height=15feet−8feet=7feet
Therefore, when the player hits the ball, it's 7 feet above the ground.
Question
A volleyball player hits the ball when it is h feet above the ground. The volleyball net is 8 feet tall. The ball lands 15 feet away from the base of the net, as shown.What is the height of the ball when the player hits it? Round to the nearest tenth of a foot.