Name
Period
Date
Motion in 2 & 3 Dimensions: WORKSHEET 1
For your solutions to these problems, show the general mathematical relationships
you may use in your solutions in algebraic form (no numbers substituted, just letters)
before putting any numbers into them. Neglect any air resistance.
1. A small ball rolls horizontally off of the edge of a tabletop that is 1.20 m high. It
strikes the floor at a point 1.52 m horizontally from the table edge.
a. How long is the ball in the air?
b. What are the vertical and horizontal
components of its speed at the instant
it leaves the table?
2. A lowly high diver pushes off horizontally with a speed of 2.00 m
s
from the platform
edge 10.0 m above the surface of the water.
a. At what horizontal distance from
b. At what vertical distance above the
the edge is the diver 0.800 s after
surface of the water is the diver just
then?
pushing off?
c. At what horizontal distance from the edge does the diver strike the water below?
Motion in 2&3-D: Worksheet 1
page 2
3. Suppose a metal sphere leaves a ramp with vo  1.5 m
vo
as
s
shown. The end of the ramp is 1.20 m above the floor.
a. Calculate the sphere’s time of flight. (You might need to
use the quadratic formula!)
20.°
1.20 m
b. Calculate the range of the sphere.
4. Now suppose that the ramp is tilted downwards as shown below. Suppose that the
sphere leaves the ramp at 1.5 m . The bottom of the ramp is 0.90m above the floor.
s
Calculate the range of the sphere.
15°
vo
0.90 m
Motion in 2&3-D: Worksheet 1
page 3
5. During a tennis match, a player serves the ball at 23.6 m , with the center of the ball
s
leaving the racquet horizontally 2.37 m above the court surface. The net is 12 m
away and 0.90 m high.
a. How long does it take the ball to
b. Does the ball clear the net? If so, by
reach the net?
how much? If not by how much does
it miss?
Suppose that instead, the ball is served as before but now it leaves the racquet at
5.0 below the horizontal.
c. How long does it now take the ball
d. Does the ball clear the net? If so, by
to reach the net?
how much? If not by how much does
it miss?
6. A soccer ball is kicked from the ground with an initial speed of 19.5 m
at an upward
s
angle of 45 . A player 55 m away in the direction of the kick starts running to meet
the ball at that instant. What must her average speed be if she is to meet the ball
just before it hits the ground?
Motion in 2&3-D: Worksheet 1
page 4
7. According to the Guinness Book of World Records, during a catastrophic explosion
at Halifax on December 6, 1917, William Becker was thrown through the air for
some 1500 m and was found, still alive, in a tree. Assume that Becker left the
ground and returned to the ground (ignore the height of the tree) at an angle of 45 .
a. What was the slowest possible speed with which he left the ground?
b. How high did he rise?
c. How long did he stay in flight?
Motion in 2&3-D: Worksheet 1
page 5
15 m/s
29
5.0 m
8. A block is moving at 15 m/s up a 6.2 m long incline at 29 as in the diagram. The
coefficient of kinetic friction between the box and the incline is  k  0.355 .
a. Draw and label all forces (not components) acting on the box as it slides up the
incline.
b. What is the acceleration of the block as it moves up the incline? If you need to
draw anything besides what you have shown in part (a) to assist in your solution,
use the space below. Do NOT add anything to the figure in part (a).
Motion in 2&3-D: Worksheet 1
page 6
c. What is the velocity (both magnitude and direction) of the box when it reaches
the top of the incline?
d. How far from the table does the box land after leaving the incline 5.0 m above
the ground as in the diagram? Assume no air resistance.