A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 23.2 m/s at an angle of 52.0° to the horizontal. Answer parts a-b.

Answers

Answer 1

(a) The ball falls short of clearing the crossbar by 3.05 m (negative value indicates falling short).

(b) The ball approaches the crossbar while falling since it doesn't reach a height greater than the crossbar's height during its trajectory.

To solve this problem, we'll analyze the vertical motion of the ball.

(a) To find how much the ball clears or falls short of clearing the crossbar vertically, we need to calculate the maximum height reached by the ball.

The initial velocity (V0) of the ball is 23.2 m/s, and the launch angle (θ) is 52.0° above the horizontal.

The vertical component of velocity (Vy) at the highest point of the trajectory is zero since the ball momentarily stops before falling back down.

To find the time taken to reach the highest point, we can use the equation:

Vy = V0 * sin(θ)

0 = 23.2 m/s * sin(52.0°)

Solving for sin(52.0°), we find:

sin(52.0°) ≈ 0.7880

Dividing both sides by 23.2 m/s, we get:

0.7880 = sin(52.0°)

Taking the inverse sine, we find:

52.0° ≈ arcsin(0.7880)

Using a calculator, we find:

52.0° ≈ 56.43°

Now we can calculate the time (t) it takes to reach the highest point using the equation:

t = (2 * Vy) / g

Since Vy = 0, we have:

t = 0

This means that the ball reaches its maximum height instantaneously and starts falling immediately. Therefore, the ball does not clear the crossbar.

To find how much the ball falls short of clearing the crossbar vertically, we can calculate the height of the ball at a horizontal distance of 36.0 m.

Using the equation for vertical displacement, we have:

Δy = V0y * t + (1/2) * g * [tex]t^2[/tex]

Plugging in the known values:

Δy = 0 * t + (1/2) * (-9.8 [tex]m/s^2[/tex]) * ([tex]t^2[/tex])

Since t = 0, the equation simplifies to:

Δy = 0

Therefore, the ball falls short of clearing the crossbar by 3.05 m vertically.

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Related Questions

Explain the function of power supply, readout, peripheral, microcomputer, transducer and processor

Answers

The function of the power supply is to provide electrical energy to the device or system that needs it. The power supply converts the incoming voltage from the power source into a form that is usable by the device, such as DC voltage.

The readout is a device or component that displays data or information to the user. The readout could be a simple LED display or a complex graphical display.

A peripheral is a device or component that connects to a computer or other electronic device to provide additional functionality. Examples of peripherals include printers, scanners, and external hard drives.

A microcomputer is a type of computer that is designed to fit on a single microchip. Microcomputers are found in a wide range of devices, including smart phones, tablets, and embedded systems.

A transducer is a device that converts one form of energy to another. In electronics, transducers are commonly used to convert electrical energy into mechanical energy, or vice versa.

The processor is the central component of a computer or electronic device. The processor is responsible for executing instructions and controlling the other components of the system. The performance and capabilities of a device are largely determined by the speed and power of the processor.

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