Physics 218 Spring 2016
Practice Midterm 1 Answers
1. A cart is moving with a constant horizontal
velocity of 5.00 m/s. A small pebble is
launched from the front of the cart with a
velocity of 8.00 m/s at 60.0∘ above the
horizontal as measured relative to the cart
(see Fig. 3.3). Just as the pebble returns to
the level from which it was launched, its
distance from the front of the cart is closest
to: 5.66 m
Hint: Think of ICE#3, Q2. The pebble’s initial velocity is same as that of the cart.
2. A toy rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine
provides constant upward acceleration during the burn phase. At the instant of engine burnout, the
rocket has risen to 82 m and acquired a velocity of 90 m/s. The rocket continues to rise in unpowered
flight, reaches maximum height, and falls back to the ground. The time interval, during which the rocket
engine provides upward acceleration, is closest to: 1.8 s
Hint: Same hint as Q1, and also of ICE#3, Q2
4. A model of a helicopter rotor has four blades, each of length 3.50 m from the central shaft to the
blade tip. The model is rotated in a wind tunnel at a rotational speed of 550 rev/min. What is the linear
speed of the blade tip?
ANSWER:
v=
= 202
m/s
Hint: Get things to same unit and use rotational to linear conversion.
5. If r⃗ =bt2i^+ct3j^, where b and c are positive constants, when does the velocity vector make an angle
of 45.0o with the x- and y-axes?
ANSWER: t=2b/3c
Hint: Simple differential to get x and y components and set them equal to each other
6. A rocket fires two engines simultaneously. One produces a thrust of 480 N directly forward, while the
other gives a 513 N thrust at 32.4 degrees above the
forward direction. Find the magnitude and direction
(relative to the forward direction) of the resultant force
that these engines exert on the rocket.
ANSWER: 954 N at an angle 16.7 degrees above the
forward direction
Hint: Vector addition
7. A snowball rolls off a barn roof that slopes downward at
an angle of 40 degree(s) . The edge of the roof is 14.0 m
above the ground, and the snowball has a speed of 7.00
m/s as it rolls off the roof. Ignore air resistance.
a) How far from the edge of the barn does the snowball
strike the ground if it doesn't strike anything else while
Physics 218 Spring 2016
Practice Midterm 1 Answers
falling?
ANSWER: x = 6.93 m
b) A man 1.9 m tall is standing 4.0 m from the edge of the barn. Will he be hit by the snowball?
ANSWER: No
8. Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due
north with a speed of 6.00 m/s. The velocity of the ball relative to Mia is 5.00 m/s in a direction 30.0
degrees east of south. What is the velocity of the ball relative to the ground?
ANSWER: 5.57 m/s at 51 degrees east of south
Hint: Relative velocity equation. Sum of Mia’s velocity and ball’s velocity relative to ground should total to
the ball’s velocity relative to Mia.
9. A lunar lander is making its descent to Moon Base I. The
lander descends slowly under the retro-thrust of its descent
engine. The engine is cut off when the lander is 5.0 m above
the surface and has a downward speed of 0.80 m/s. With the
engine off, the lander is in free fall.
a) What is the speed of the lander just before it touches the
surface? The acceleration due to gravity on the moon
is 1.6m/s2.
ANSWER: v = 4.1 m/s
Hint: Like question 1, think about the initial velocity of the lander
10. The earth has a radius of 6380 km and turns around once on its axis in 24 h.
a) What is the radial acceleration of an object at the earth's equator? Give your answer in m/s2 and as
fraction of g.
-2
2
-3
ANSWER: arad = 3.4 x 10 m/s or 3.40 x 10 g
b) If arad at the equator is greater than g, objects would fly off the earth's surface and into space. What
would the period of the earth's rotation have to be for this to occur?
ANSWER: T = 5070 s
Hint: Straightforward use of circular motion equations