Problem 1: A man throws a ball upwards giving it an initial speed of v 0 = 50 me
ID: 585303 • Letter: P
Question
Problem 1: A man throws a ball upwards giving it an initial speed of v0 = 50 meters/ second. The ball has a mass of 10 kg
and is released at a height of x0 = 4 meters above the ground. The height h of greatest ascent above the ground is:
a) 25 meters
(b) 54 meters
(c) 129 meters
(d) 254 meters
(e) 379 meters
Problem 2: In still water a man can row a boat 5 miles per hour. In what direction must he point to travel perpendicular to
the flow of the stream? (See Fig. 2). Assume the stream flows in the positive x direction at a speed of 2 miles per hour. Give your
answer in terms of the angle j.
Problem 3: A cannonball is fired with an initial speed of jv0j = 400 ft/s from a cannon located at position (x1 = 1.5 m, y1 =
3 m). The cannon angled such that j = 20. (See Fig. 3)
(a) Determine the maximum height obtained by the ball.
(b) Determine the the horizontal range (maximum horizontal distance from x1).
Problem 4: A car drives around a circular track as shown in Fig. 4. The car is moving with a constant speed of 70 miles per
hour. Which one of the following statements is true:
(a) the car is never accelerating
(b) the car is always accelerating
Problem 6: Let
~r1 = 4 ^ex + 3 ^ey + 8 ^ez
~r2 = 2 ^ex + 10 ^ey + 5 ^ez
(a) Find the magnitude of~r1 and~r2.
(b) Calculate the angle bewteen~r1 and~r2.
(c) Calculate the projection of~r1 on~r2.
(d) Calculate the vector product~r1 ~r2.
Problem 7: A train is traveling eastbound at a constant speed of v0 = 100 m/ s (see Fig. 5). How much distance does the
train cover in one minute?
(a) 1.6 meters
(b) 100 meters
(c) 600 meters
(d) 6, 000 meters
(e) 360, 000 meters
Problem 8: A helicopter is initially traveling westbound at a constant speed of v0 = 80 m/ s (see Fig. 6). The helicopter
begins to accelerate at time t = 0 with a constant acceleration of magnitude a = 10 m/ s2. Determine the speed of the helicopter
at time t = 60 sec.
(a) 520 m/ s
(b) 600 m/ s
(c) 680 m/ s
(d) 800 m/ s
(e) 48, 000 m/ s
Problem 9: An average speed is constant over the time interval in which it was calculated.
(a) True
(b) False
initial conditions xo = initial height U0 initial speed direction arrowsExplanation / Answer
1) As v^2 = u^2 - 2gS ====> S = u^2/2g = 50^2/2*10 = 125 m
So H = S + x0 = 125+4 = 129 m (Option C)
3) a) v= 400 ft/s = 121.92 m/s
Maximum Height = Vy^2/2g = (121.92*sin20)^2/20 = 86.94 m
So, the maximum height obtained by the ball from ground = 86.94 + 3.0 = 89.94 m
b) Time of flight = 2Vy/g = 2*121.92*sin20/10 = 8.34 s
Horizontal Range = 121.92*cos20*8.34 = 955.5 m (from x1)
4) The car is always accelerating as centripetal force is always there.
7) The distance covered by train in one minute = 100*60 = 6000 m (option d)
8) As v = u + at = 80 + 10*60 = 680 m/s (option C)
Note: At one time I can do only 4-5 problems.