Physics-Projectile motion exercises

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A ball is thrown skywards with an initial vertical velocity of 24 m/s and an initial horizontal velocity of 10 m/s as shown on the right. Ignore air resistance
a) What is the initial velocity of the ball? The initial velocity of the ball can be calculated by adding the horizontal and vertical velocity vectors. Using the Pythagorean Theorem we calculate the magnitude of the resulting vector. X² = 24² + 10^{2 X = square root (676) = 26 So the initial velocity of the ball is 26 km/hr}
b) How long does the ball take to reach its maximum height? Assuming g =10 m/s/s/. Don't forget that the horizontal and vertical velocities are independent. Height is determined by the vertical velocity. Gravity acts to slow the ball at a rate of 10 m/s/s. So every second the ball's velocity decreases by 10m/s. It will take 2.4 seconds for the ball to reach its maximum height.
c) What is the maximum height reached by the ball? To answer this question we use our straight line motion formulae. Click to revise. Distance is given by the formula d = (1/2)at² . Where d = distance, a =10 m/s/s/ and t = time. d = (1/2)10 (2.4)² = 28.8 m
d) How far does the ball land from the thrower? The horizontal distance is determined by the horizontal velocity component. We use the formula d = vt, where v = velocity, t = time. The ball takes 2.4 seconds to reach its maximum height and a further 2.4 seconds to reach the ground. It is in the air for 4.8 seconds. So d = 10 m/s X 4.8 = 48 m
e) What is the magnitude of the velocity of the ball at "A"? At the top of its path vertical velocity has shrunk to zero while the horizontal velocity remains constant throughout the entire flight. The velocity is 10 m/s.
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A ball is thrown skywards with an initial vertical velocity of 40 m/s and an initial horizontal velocity of 8 m/s as shown on the right. Ignore air resistance a) What is the initial velocity of the ball? b) How long does the ball take to reach its maximum height? c) What is the maximum height reached by the ball? d) What is the balls vertical acceleration? e) What is its horizontal acceleration? f) At what point along its path does the ball have minimum speed?
a) What is the initial velocity of the ball? The initial velocity is obtained by adding the two component velocity vectors. 40.84 m/s
b) How long does the ball take to reach its maximum height? The decelerates at 10 m/s/s. So every second the ball will slow down by 10 m/s. Therefore it will take 4 seconds for the ball to reach maximum height.
c) What is the maximum height reached by the ball? We use the formula d = 1/2at² , where d =distance, a = 10 m/s/s and t = 4s. d = 1/2 X 10 X 16 = 80m
d) What is the ball's vertical acceleration? Gravity accelerates the ball at -10m/s/s. It slows the ball down 10 m/s every second.
d) What is the ball's horizontal acceleration? The horizontal velocity remains constant so horizontal acceleration is zero.
f) At what point along its path does the ball have minimum speed? At its maximum height the vertical velocity shrinks to zero leaving only the horizontal velocity which remains constant throughout the flight. At this point ("A") the ball has a velocity of only 8 m/s.
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Both balls have a vertical acceleration component of 10m/s/s (assuming g =10 m/s/s). Since vertical motion is independent of horizontal motion both balls will hit the ground at the same time.

Projectile motion Exercises
A ball is thrown skywards with an initial vertical velocity of 24 m/s and an initial horizontal velocity of 10 m/s as shown on the right. Ignore air resistance a) What is the initial velocity of the ball? b) How long does the ball take to reach its maximum height? Assume g=10m/s/s/. c) What is the maximum height reached by the ball? d) How far does the ball land from the thrower? e) What is the magnitude of the velocity of the ball at "A"? Solution
A ball is thrown skywards with an initial vertical velocity of 40 m/s and an initial horizontal velocity of 8 m/s as shown on the right. Ignore air resistance a) What is the initial velocity of the ball? b) How long does the ball take to reach its maximum height? c) What is the maximum height reached by the ball? e) What is the balls vertical acceleration? f) What is its horizontal acceleration? g) At what point along its path does the ball have minimum speed? Solution
A ball is hurled horizontally off the table with a velocity of 20m/s while another identical ball is allowed to fall, from the top of the table to the floor. Which ball strikes the ground first? Solution Explain why? Solution
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