Section 3 review
Projectiles move horizontally at uniform velocity and vertically, accelerated by gravity. The motions can be analyzed separately, and this is the key to solving problems, such as a projectile’s range or time of flight. Motion along a ramp is accelerated by gravity if the ramp is inclined: the steeper the angle, the greater the acceleration. Rolling friction reduces this acceleration, but is less significant as the ramp steepens. Read the text aloud
trajectory, projectile, range, inclined plane, ramp coordinates

x= v x0 t v x = v x0
y= v y0 t 1 2 g t 2 v y = v y0 gt
x= v 0 t cosθ v x = v 0 cosθ
y= v 0 tsinθ 1 2 g t 2 v y = v 0 sinθgt
x= 2 v 0 2 sinθcosθ g
a ramp =( h L )g
a x =gsinθ
a x =g(sinθ μ r cosθ)

Review problems and questions

The soccer ball is kicked with initial speed <i>v</i><sub>0</sub> at an angle <i>θ</i> with the ground
  1. A soccer ball is kicked and leaves the ground with an initial speed v0 at an angle θ. Assume that the initial speed is fixed but the angle can vary. Match each quantity in the left-hand column with one quantity in the right-hand column:
    time ball is in airlargest when θ = 0°
    horizontal speedlargest when 0 < θ < 90°
    horizontal distancelargest when θ = 90°
    Read the text aloud Show
  1. A soccer ball is kicked at an upward angle θ between 0° and 90°. Its initial vertical (y) velocity vy0 is 19.6 m/s. It follows a parabolic trajectory and lands at the end of its range.
    1. How long (how much time) is the ball in the air?
    2. How high does the ball get?
    3. If the ball’s range is 60 m, is the angle θ less than, equal to, or greater than 45°? Read the text aloud Show
Toy car is placed on a two meter long ramp
  1. A small toy car is placed upon a ramp that is 2 m long. The car is released (with zero initial velocity) from the top of the ramp. Assume that friction is negligible.
    1. How high is the top if the car takes 2.0 s to reach the bottom?
    2. Now suppose that you want the car to go from top to bottom in just one second (and you are still releasing it, not pushing it, so its initial velocity remains zero). In other words, you want to divide the travel time by two. Will you achieve this by doubling the height, or will you have to raise the ramp by a different amount? Read the text aloud Show

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