Hillary kicks a ball so that it is in the air for 3.2 s. The ball lands down field 56 m from its starting point.
a. Determine the x and y velocities of the ball.
If it is in the air 3.2 s, it spends half of that time, T = 1.6 s coming back down.
Vy = g T = 15.68 m/s
The horizontal velocity componebt is
Vx = 56m/3.2s = 17.50 m/s
To determine the x and y velocities of the ball, we need to break down the motion of the ball into horizontal (x-axis) and vertical (y-axis) components.
Let's assume the initial velocity of the ball, which includes both the x and y components, is represented by v0. We can split this initial velocity into its x and y components using trigonometry.
Let's say the angle at which Hillary kicked the ball is represented by θ. We can use the following trigonometric relationships:
vx = v0 * cos(θ)
vy = v0 * sin(θ)
Next, let's find the y-velocity component. We can use the kinematic equation:
y = v0y * t - (1/2) * g * t^2
In this equation, y represents the vertical displacement (upward or downward) of the ball, t represents the time the ball is in the air, and g represents the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the ball is in the air for 3.2 s, we can substitute the values into the equation to solve for v0y:
0 = v0y * 3.2 - (1/2) * 9.8 * (3.2)^2
Solving this equation will give us the value of v0y.
Now let's find the x-velocity component. We know that the horizontal displacement (distance traveled in the x-direction) is 56 m. We can use the equation:
x = v0x * t
Given that the time is 3.2 s and the horizontal displacement is 56 m, we can solve this equation for v0x.
Once we have the values of v0x and v0y, we will have determined the x and y velocities of the ball.