Problem Set 2 : Kinematics
1. Instructions for finding a buried treasure include the following: Go 75.0 paces at 240°, turn
to 135° and walk 125 paces, then travel 100 paces at 160°. The angles are measured
counterclockwise from an axis pointing to the east, the +x direction. Determine the
resultant displacement from the starting point.
2. In a game of American football, a quarterback takes the ball from the line of scrimmage,
runs backward a distance of 10.0 yards, and then sideways parallel to the line of scrimmage
for 15.0 yards. At this point, he throws a forward pass 50.0 yards straight downfield
perpendicular to the line of scrimmage. What is the magnitude of the football’s resultant
displacement?
3. A displacement vector lying in the xy plane has a magnitude of 50.0m and is directed at an
angle of 120° to the positive x axis. What are the rectangular components of this vector?
4. Batman and Robin are out riding their batcycles. Batman is driving his at 80 km/h. Robin is
just passing batman at 100 km/h when they both see a log lying directly across the road in
front of them. The two batcycles are precisely abreast when both brake hard, with equal
constant deceleration. Batman stops just millimeters from the log. With what speed does
Robin strike the log?
5. A stream of water from the nozzle of a hose emerges horizontally with a speed of 12 m/s. If
the water strikes the ground 0.5 seconds later, how high is the nozzle above the ground?
What is the horizontal range of the water?
6. A homerun in a baseball game is hit in such a way that the ball just clears a wall 21 m high,
located 130 m from home plate. The ball is hit at an angle of 35° to the horizontal, and air
resistance is negligible. Find :
a. The initial speed of the ball
b. The time it takes for the ball to reach the wall
c. The velocity components of the ball at the wall
7. An astronaut on a strange planet finds that she can jump a maximum range of 30 m when
she jumps with an initial speed of 9 m/s. What is the acceleration due to gravity on the
planet?
8. Our student council president, in a fit of rage, throws a rotten pineapple into the air with an
initial velocity of 30 m/s, at an angle of 56° above the horizontal. Calculate :
a. The maximum height reached by the pineapple
b. The total time the pineapple is in flight
c. The velocity components of the pineapple at the ground
d. The total final velocity of the pineapple
9. It seems reasonable that in order to attain the maximum possible range for any projectile
that it should be projected at an angle of 45°. Prove this mathematically (NB : trial and error
is not a valid proof)
10. A daredevil is shot out of a cannon at an angle of 45°, with an initial speed of 25 m/s. A net
is located a horizontal distance of 50 m from the cannon. AT what height above the cannon
should the net be placed in order to catch the daredevil?
11. The Green Goblin climbs to the top of the Baxter building, 15 m above the ground, and lobs
a pumpkin bomb into the air. The Goblin is able to toss the bomb at an angle of 60° along a
perfect parabolic path. Spiderman notes that it takes exactly 2.6 seconds for the pumpkin
bomb to reach maximum height. Find :
a. The initial speed of the pumpkin bomb
b. The horizontal range of the projectile
c. The total time in flight for the projectile
12. A ball is thrown from the top of a 35 m high building and strikes the ground a horizontal
range of 80 m from the base of the building. Find :
a. The time in flight for the ball
b. The initial speed of the ball
c. The x and y components of the final velocity of the ball
13. A car is parked on a steep incline overlooking the ocean. The incline makes an angle of 37°
with the horizontal. The negligent driver leaves the car in neutral and the parking brake is
defective. The car rolls from rest down the incline with a constant acceleration of 4 m/s2
traveling the 40 m towards the edge of the incline. The cliff is 30 m above the ocean. Find :
a. The speed of the car when it reaches the edge of the incline
b. The time it takes to reach the edge of the incline
c. The velocity of the car when it lands in the ocean
d. The distance the car lands from the base of the cliff
14. A Zehrs truck loaded with cannonball watermelons stops suddenly to avoid running over the
edge of a washed out bridge. The quick stop causes a number of melons to fly off of the
truck. One melon rolls over the edge of the road with an initial velocity of 10 m/s in the
horizontal direction. The river valley has a parabolic cross-section matching the equation
y2=16x where x and y are measured in metres with the vertex at the road edge. What are
the x and y components of where the watermelon smashes onto the river valley?
15. A cannon is placed at the foot of a long sloped linear hill. The hill has a +10° grade. The
cannon is angled so that it is 30° above the inclined surface and a cannon ball is fired with a
speed of 10 m/s. What is the vertical displacement of the cannonball when it impacts the
incline.