Question

A placekicker is attempting to make a 64 yard field goal. If the launch angle of the football is 40 degrees, what is the minimum initial speed u which will allow the kicker to succeed if the goal post is 10 foot tall?

Answer 1

The minimum initial speed is 105.3feet/second

The horizontal distance traveled by the football (range) can be calculated using the formula:

Range = u² sin(2θ)/g

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where:

• u = initial speed,

• θ = launch angle in radians (40 degrees converted to radians is approximately
• g = acceleration due to gravity (approximately 32.2 feet/s²).

Given the range is 192 feet and the goal post is 10 feet tall, the minimum initial speed required for the ball to pass over the goal post is determined by solving the range equation for

u = √Range × g/sin (2θ)

Substitute the values, we get;

u = √192 ×32.2/sin (2 ×π ×40/180)

​u = 105.3feet/second