A Study on Projectile Motion of Tennis Ball Launched from a Spring-loaded Cannon

Understanding Projectile Motion

A small, spring-loaded cannon launches a tennis ball from level ground with an initial speed vi at an angle θi with the horizontal. The tennis ball lands a horizontal distance R from its launch point. The highest point the tennis ball reaches during its flight is a distance R 12 above the ground. In terms of R and g, find the following:

(a) Time Interval During Motion

The time interval during which the tennis ball is in motion can be calculated as: T = (2vi sinθ) / g

(b) Speed at the Peak of Path

The tennis ball's speed at the peak of its path is: vi cosθi

(c) Initial Vertical Component of Velocity

The initial vertical component of the tennis ball's velocity is: vi sinθi

What is Projectile Motion?

Projectile motion is the motion of the body when thrown in the air, influenced by the action of gravity. Given information: - Initial speed of the ball: vi - Distance traveled by the tennis ball: R - Angle of projection: θi

Calculations:

(a) Time Interval During Motion

The time interval during which the tennis ball is in motion, also known as time of flight, is given by: T = (2vi sinθ) / g

(b) Speed at the Peak of Path

At the peak of its path, the tennis ball's speed is equal to the horizontal component of velocity: vp = vx = vi cosθi

(c) Initial Vertical Component of Velocity

The initial vertical component of the tennis ball's velocity is: vy = vi sinθi In conclusion, the time interval, speed at the peak of path, and initial vertical component of velocity for the tennis ball in projectile motion can be determined using the above calculations.

What are the key factors to consider when analyzing the projectile motion of a tennis ball launched from a spring-loaded cannon?

The key factors to consider when analyzing the projectile motion of a tennis ball include the initial speed, angle of projection, distance traveled, and the effects of gravity on the motion. Additionally, considering air resistance and the height of the launch point are crucial for accurate analysis.

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