Question

A soccer ball, kicked from ground level at an angle of 64.0° above horizontal, is in the air for 3.40 s. What was its initial speed, in m/s, just after it was kicked? Ignore air resistance.

Answer 1

To find the initial speed of the soccer ball, we can use the equations of projectile motion. By breaking down the initial velocity into horizontal and vertical components, we can calculate the horizontal distance and initial speed of the ball. The initial speed can be found using the equation v0 = d / (v0 * cos(θ))

Step-by-step explanation:

To solve this problem, we can use the equations of projectile motion. Since the soccer ball is kicked at an angle above the horizontal, we can break down its initial velocity into horizontal and vertical components. The vertical component will determine the maximum height reached by the ball, while the horizontal component will determine how far the ball travels horizontally.

The initial speed of the ball can be calculated by using the equation:

v0,x = v0 * cos(θ)

where v0,x is the horizontal component of the initial velocity, v0 is the initial speed, and θ is the angle above the horizontal.

Using the given information, we can substitute the values into the equation:

v0,x = v0 * cos(64.0°)

Since the ball is in the air for 3.40 s, we can also calculate the horizontal distance traveled by the ball using the equation:

d = v0,x * t

where d is the horizontal distance, v0,x is the horizontal component of the initial velocity, and t is the time the ball is in the air.

By substituting the values into the equation, we can solve for the initial speed:

v0 = d / (v0 * cos(θ))

Now we can calculate the initial speed:

v0 = (d) / (v0,x * cos(64.0°))