player kicks football from ground level with velocity of32 m/s at an angle of 40 degrees above horizontal. What is hang time of football?
How far does the ball travel horizontally before hitting the ground?
What is the maximum height that the ball reaches?
Resolve the kickoff velocity into the horizontyal components Vx = 32 cos 40 and vertica component Vy = 32 sin 40.
There are formulas that relate the hang time (T) and the maximum height (H) to Vy. Get to know them.
Vy = sqrt(2 g H)
T*g = Vy
The "hang time" T times Vx is the distance the ball travels horizontaly before hitting gthe ground.
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To find the hang time of the football, you can use the vertical component of the initial velocity and the acceleration due to gravity. The hang time is the time it takes for the football to reach its maximum height and then return to the ground.
Step 1: Calculate the vertical component of the initial velocity:
Vertical Component of Velocity (Vv) = Initial Velocity (V) * sin(angle)
Vv = 32 m/s * sin(40°)
Step 2: Calculate the time it takes to reach the maximum height:
Use the kinematic equation: Vf = Vi + at, where Vf = 0 m/s (at the maximum height) and a = -9.8 m/s² (acceleration due to gravity).
0 = Vv + (-9.8 m/s²)t
t = -Vv / (-9.8 m/s²)
Step 3: Calculate the total hang time:
Since the ball takes the same amount of time to reach the maximum height and return to the ground, the total hang time is twice the time calculated in step 2.
Hang Time = 2 * t
To find the horizontal distance the ball travels before hitting the ground, you can use the horizontal component of the initial velocity and the total hang time.
Step 4: Calculate the horizontal component of the initial velocity:
Horizontal Component of Velocity (Vh) = Initial Velocity (V) * cos(angle)
Vh = 32 m/s * cos(40°)
Step 5: Calculate the horizontal distance:
Use the equation: Distance (D) = Velocity (V) * Time (T)
D = Vh * Hang Time (from step 3)
To find the maximum height that the ball reaches, you can use the vertical component of the initial velocity and the time it takes to reach the maximum height.
Step 6: Calculate the maximum height:
Use the equation: Distance (D) = Velocity (V) * Time (T) + 0.5 * Acceleration (a) * Time (T)²
0 = Vv * t + 0.5 * (-9.8 m/s²) * t²
Solve the quadratic equation to find t. Then, substitute the value of t into the equation to find the maximum height.
Remember to convert angles to radians if necessary.
Plug in the given values of initial velocity (32 m/s) and angle (40°) to find the hang time, horizontal distance, and maximum height of the ball.