1. In the figure, particle A moves along the line y = 33 m with a constant velocity vector V of magnitude 2.9 m/s and directed parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration vector A of magnitude 0.48 m/s2. What angle θ between vector A and the positive direction of the y axis would result in a collision?
Number: 53.04 Units: Degrees
2. Flying Circus of Physics
In the 1991 World Track and Field Championships in Tokyo, Mike Powell jumped 8.95 m, breaking by a full 5 cm the 23-year long-jump record set by Bob Beamon . Assume that Powell’s speed on takeoff was 9.5 m/s (about equal to that of a sprinter) and that g = 9.80 m/s2 in Tokyo. How much less was Powell’s horizontal range than the maximum possible horizontal range for a particle launched at the same speed?
Number: 0.26 Units: m
3. A soccer ball is kicked from the ground with an initial speed v at an upward angle θ. A player a distance d away in the direction of the kick starts running towards the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground? Give your answer in terms of g and the given variables (neglecting air resistance).
4. In the figure, you throw a ball toward a wall at speed 31.0 m/s and at angle θ0 = 38.0˚ above the horizontal. The wall is distance d = 18.0 m from the release point of the ball. (a) How far above the release point does the ball hit the wall? What are the (b) horizontal and (c) vertical components of its velocity as it hits the wall?
a. 11.40 Unit: m
b. 24.43 Unit: m/s
c. 11.86 Unit: m/s
Flying Circus of Physics
5. In 1939 or 1940, Emanuel Zacchini took his human-cannonball act to an extreme: After being shot from a cannon, he soared over three Ferris wheels and into a net (see the figure). Assume that he is launched with a speed of 26 m/s and at an angle of 48°. (a) Treating him as a particle, calculate his clearance over the first wheel. (b) If he reached maximum height over the middle wheel, by how much did he clear it? (c) How far from the cannon should the net’s center have been positioned (neglect air drag)?
a. 5.93 Units: m
b. 7.05 Units: m
c. 68.61 Units: m
6. A boat is traveling upstream at 10 km/h with respect to the water of a river. The water is flowing at 9.0 km/h with respect to the ground. What are the (a) magnitude and (b) direction of the boat’s velocity with respect to the ground? A child on the boat walks from front to rear at 5.0 km/h with respect to the boat.What are the (c) magnitude and (d) direction of the child’s velocity with respect to the ground?
a. 1 Units: Km/h
c. 4 Units:Km/h
7. Two highways intersect as shown in the figure. At the instant shown, a police car P is distance dP = 850 m from the intersection and moving at speed vP = 85 km/h. Motorist M is distance dM = 510 m from the intersection and moving at speed vM = 51 km/h. What are the (a) x-component and (b) y-component of the velocity of the motorist with respect to the police car? (c) For the instant shown in the figure, what is the angle between the velocity found in (a) and (b) and the line of sight between the two cars?
a. 85 Units: Km/h
b. -51 Units: Km/h
c. 0 Units: degrees
8. A 370-m-wide river has a uniform flow speed of 1.3 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 5.8 m/s with respect to the water. There is a clearing on the north bank 58 m upstream from a point directly opposite the clearing on the south bank. (a) At what angle, measured relative to the direction of flow of the river, must the boat be pointed in order to travel in a straight line and land in the clearing on the north bank? (b) How long will the boat take to cross the river and land in the clearing?
a. 111.70 Units: degrees
b. 68.66 Units: s
9. A particle P travels with constant speed on a circle of radius r = 3.40 m (see the figure) and completes one revolution in 20.0 s. The particle passes through O at time t = 0.
At t = 5.00 s, what is the particle’s position vector? Give (a) magnitude and (b) direction (as an angle relative to the positive direction of x.
At t = 7.50 s, what is the particle’s position vector? Give (c) magnitude and (d) direction (as an angle relative to the positive direction of x.
At t = 10.00 s, what is the particle’s position vector? Give (e) magnitude and (f) direction (as an angle relative to the positive direction of x.
For the 5.00 s interval from the end of the fifth second to the end of the tenth second, find the particle’s displacement. Give (g) magnitude and (h) direction (as an angle relative to the positive direction of x.
For that interval, find its average velocity. Give (i) magnitude and (j) direction (as an angle relative to the positive direction of x.
For that interval, find its velocity at the beginning. Give (k) magnitude and (l) direction (as an angle relative to the positive direction of x.
For that interval, find its velocity at the end of the interval. Give (m) magnitude and (n) direction (as an angle relative to the positive direction of x.
Find the acceleration at the beginning of that interval. Give (o) magnitude and (p) direction (as an angle relative to the positive direction of x.
Next, find the acceleration at the end of that interval. Give (q) magnitude and (r) direction (as an angle relative to the positive direction of x.
a. 4.81 Units: m
b. 45 Units: degrees
c. 6.28 Units: m
d. 67.50 Units: degrees
e. 6.8 Units: m
f. 90 Units: degrees
g. 4.81 Units: m
h. 135 Units: degrees
i. 0.962 Units: m/s
j. 135 Units: degrees
k. 1.07 Units: m/s
l. 90 Units: degrees
m. 1.07 Units: m/s
n. 180 Units: degrees
o. 0.34 Units: m/s^2
p. 180 Units: degrees
q. 0.34 Units: m/s^2
r. 270 Units: degrees
10. The fast French train known as the TGV (Train à Grande Vitesse) has a scheduled average speed of 216 km/h. (a) If the train goes around a curve at that speed and the magnitude of the acceleration experienced by the passengers is to be limited to 0.050g, what is the smallest radius of curvature for the track that can be tolerated? (b) At what speed must the train go around a curve with a 1.01 km radius to be at the acceleration limit?
a. 7.35 Units: km
b. 80.09 Units: km/h