College Physics 3.51 – Construct Your Own Problem


Consider a ball tossed over a fence. Construct a problem in which you calculate the ball’s needed initial velocity to just clear the fence. Among the things to determine are; the height of the fence, the distance to the fence from the point of release of the ball, and the height at which the ball is released. You should also consider whether it is possible to choose the initial speed for the ball and just calculate the angle at which it is thrown. Also, examine the possibility of multiple solutions given the distances and heights you have chosen.


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College Physics 3.50 – Unreasonable Results


(a) Find the maximum range of a super cannon that has a muzzle velocity of 4.0 km/s.
(b) What is unreasonable about the range you found?
(c) Is the premise unreasonable or is the available equation inapplicable? Explain your answer.
(d) If such a muzzle velocity could be obtained, discuss the effects of air resistance, thinning air with altitude, and the curvature of the Earth on the range of the super cannon.


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College Physics 3.49 – Derive the range of a projectile on a level ground


Derive R=\frac{v_o^2\sin 2\theta _o}{g} for the range of a projectile on level ground by finding the time t at which y becomes zero and substituting this value of t into the expression for x−x0, noting that R=x−x0


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College Physics 3.48 – Prove that the trajectory of a projectile is parabolic


Prove that the trajectory of a projectile is parabolic, having the form y=ax+bx2 . To obtain this expression, solve the equation x=v0xt for t and substitute it into the expression for y=v0yt–(1/2)gt2 (These equations describe the x and y positions of a projectile that starts at the origin.) You should obtain an equation of the form y=ax+bx2 where a and b are constants.


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College Physics 3.47 – A football player punts the ball at a 45.0º angle


A football player punts the ball at a 45.0º angle. Without an effect from the wind, the ball would travel 60.0 m horizontally.
(a) What is the initial speed of the ball?
(b) When the ball is near its maximum height it experiences a brief gust of wind that reduces its horizontal velocity by 1.50 m/s. What distance does the ball travel horizontally?


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College Physics 3.46 – A basketball player jumps for a dunk


A basketball player is running at 5.00 m/s directly toward the basket when he jumps into the air to dunk the ball. He maintains his horizontal velocity.
(a) What vertical velocity does he need to rise 0.750 m above the floor?
(b) How far from the basket (measured in the horizontal direction) must he start his jump to reach his maximum height at the same time as he reaches the basket?


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College Physics 3.45 – The initial speed of a shot put for maximum distance


In 2007, Michael Carter (U.S.) set a world record in the shot put with a throw of 24.77 m. What was the initial speed of the shot if he released it at a height of 2.10 m and threw it at an angle of 38.0º above the horizontal? (Although the maximum distance for a projectile on level ground is achieved at 45º when air resistance is neglected, the actual angle to achieve maximum range is smaller; thus, 38º will give a longer range than 45º in the shot put.)


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College Physics 3.44 – A free throw shot of a basketball player


The free throw line in basketball is 4.57 m (15 ft) from the basket, which is 3.05 m (10 ft) above the floor. A player standing on the free throw line throws the ball with an initial speed of 8.15 m/s, releasing it at a height of 2.44 m (8 ft) above the floor. At what angle above the horizontal must the ball be thrown to exactly hit the basket? Note that most players will use a large initial angle rather than a flat shot because it allows for a larger margin of error. Explicitly show how you follow the steps involved in solving projectile motion problems.


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College Physics 3.43 – A goalkeeper kicking a soccer ball into the opponent’s goal


Can a goalkeeper at her/ his goal kick a soccer ball into the opponent’s goal without the ball touching the ground? The distance will be about 95 m. A goalkeeper can give the ball a speed of 30 m/s.


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College Physics 3.42 – A soccer player kicks the ball toward the goal


Suppose a soccer player kicks the ball from a distance 30 m toward the goal. Find the initial speed of the ball if it just passes over the goal, 2.4 m above the ground, given the initial direction to be 40º above the horizontal.


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