Question

In a football game, a punter kicks a ball from the goal line at 60.0° from the horizontal at 25.0 m/s. a) What is the hang time of the punt? [4.41 s] b) How far down field does the ball land? [55.2 m]

a) Hang time: 3.2 s, Distance: 35.6 m
b) Hang time: 4.41 s, Distance: 55.2 m
c) Hang time: 2.5 s, Distance: 42.0 m
d) Hang time: 5.0 s, Distance: 68.3 m

Answer 1

To find the initial speed of a football punted at a 45.0° angle that travels 60.0 m, we use the range formula for projectile motion. The initial speed can be calculated by solving the rearranged formula with the known range and angle. If the ball is affected by the wind, reducing its horizontal velocity, the new horizontal distance is calculated by multiplying the reduced velocity by the hang time.

Step-by-step explanation:

To calculate the initial speed of a football punted at a 45.0° angle, we can use the range formula for projectile motion which is R = (v^2 * sin(2θ)) / g, where R is range, v is initial speed, θ is launch angle, and g is acceleration due to gravity. Given the horizontal distance (R) is 60.0 m and the angle is 45.0°, we can solve for the initial speed v by rearranging the formula to v = √(g * R / sin(2θ)). Plugging in the values, g = 9.8 m/s^2, and sin(2 * 45.0°) = sin(90°) = 1, we obtain the initial speed.

For part (b), considering the horizontal velocity is reduced by the wind, the new horizontal velocity becomes v_x - Δv (where Δv is the velocity reduction by the wind). The new distance traveled horizontally would then be the time in the air multiplied by this new reduced horizontal velocity.