# 3.3 Projectile motion  (Page 7/16)

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## Conceptual questions

Answer the following questions for projectile motion on level ground assuming negligible air resistance (the initial angle being neither $\text{0º}$ nor $\text{90º}$ ): (a) Is the velocity ever zero? (b) When is the velocity a minimum? A maximum? (c) Can the velocity ever be the same as the initial velocity at a time other than at $t=0$ ? (d) Can the speed ever be the same as the initial speed at a time other than at $t=0$ ?

Answer the following questions for projectile motion on level ground assuming negligible air resistance (the initial angle being neither $\text{0º}$ nor $\text{90º}$ ): (a) Is the acceleration ever zero? (b) Is the acceleration ever in the same direction as a component of velocity? (c) Is the acceleration ever opposite in direction to a component of velocity?

For a fixed initial speed, the range of a projectile is determined by the angle at which it is fired. For all but the maximum, there are two angles that give the same range. Considering factors that might affect the ability of an archer to hit a target, such as wind, explain why the smaller angle (closer to the horizontal) is preferable. When would it be necessary for the archer to use the larger angle? Why does the punter in a football game use the higher trajectory?

During a lecture demonstration, a professor places two coins on the edge of a table. She then flicks one of the coins horizontally off the table, simultaneously nudging the other over the edge. Describe the subsequent motion of the two coins, in particular discussing whether they hit the floor at the same time.

## Problems&Exercises

A projectile is launched at ground level with an initial speed of 50.0 m/s at an angle of $30.0º$ above the horizontal. It strikes a target above the ground 3.00 seconds later. What are the $x$ and $y$ distances from where the projectile was launched to where it lands?

$\begin{array}{lll}x& =& \text{1.30 m}×{10}^{2}\\ y& =& \text{30}\text{.9 m.}\end{array}$

A ball is kicked with an initial velocity of 16 m/s in the horizontal direction and 12 m/s in the vertical direction. (a) At what speed does the ball hit the ground? (b) For how long does the ball remain in the air? (c)What maximum height is attained by the ball?

A ball is thrown horizontally from the top of a 60.0-m building and lands 100.0 m from the base of the building. Ignore air resistance. (a) How long is the ball in the air? (b) What must have been the initial horizontal component of the velocity? (c) What is the vertical component of the velocity just before the ball hits the ground? (d) What is the velocity (including both the horizontal and vertical components) of the ball just before it hits the ground?

(a) 3.50 s

(b) 28.6 m/s (c) 34.3 m/s

(d) 44.7 m/s, $50.2º$ below horizontal

(a) A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a $\text{32º}$ ramp at a speed of . How many buses can he clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are 20.0 m long? (b) Discuss what your answer implies about the margin of error in this act—that is, consider how much greater the range is than the horizontal distance he must travel to miss the end of the last bus. (Neglect air resistance.)

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