PHY 251 TEST 1 FA23 (1)

PHY 251 TEST 1 FA 23 Name:__________________ You will use the PHY 251 Formula Sheet (found in Course Resources), calculator, and blank paper. 1. _____Which one of the quantities below has dimensions equal to [ML/T 2 ] ? A. mv 2 B. mv 2 /r C. mv D. mv 2 /r 2 E. mrv 2. _____The mass of the Earth is 5.98 x 10 24 kg and its radius is 6.38 x 10 6 m. Using significant figure rules, what is the average density of the Earth? A. 4.676 x 10 10 kg/m 3 B. 5.50 x 10 42 kg/m 3 C. 5.497 x 10 3 kg/m 3 D. 3.665 x 10 3 kg/m 3 3. _____When applying the equations of kinematics for an object moving in one dimension, which of the following must be true? A. The velocity of the object must remain constant. B. The velocity of the object must increase with time. C. The position of the object must increase with time. D. The acceleration of the object must remain constant. E. The velocity of the object must always be in the same direction as its acceleration. 4. _____A juggler throws fruit straight up in the air. After the fruit leaves their hand and while it is in the air, which statement is true? A. The velocity of the fruit is always in the same direction as its acceleration. B. The acceleration of the fruit is zero at the top of the motion. C. The velocity of the fruit is never in the same direction as its acceleration. D. The velocity of the fruit is opposite its acceleration on the way up. E. The velocity of the fruit is in the same direction as its acceleration on the way up. 5. _____ When using the propagation of error relationship: the Δ terms, the lower-case letters, and the terms in the denominators describe respectively: A. uncertainty of a measurement, exponent of the term in the relationship, and the average of repeated measurements. B. change in measurement, exponent of the term in the relationship, and the average of repeated measurements. C. uncertainty of a measurement, exponent of the term in the relationship, and the unit vector measurement. Show your work on separate paper to support your answers and receive partial credit. Circle your final answers and make sure to include units. Correct answers with no work shown may not receive full credit. Multiple Choice = 3pts. Each.

6. _____ Applying the propagation of uncertainty relationship to determine the uncertainty in the density of a sphere given the mass, M and diameter, D the calculation will look like: A. B. C. D. 7. _____ Given a function for position versus time for a particle moving along the x axis, x = (8.5t – 2.5 t 2 ) where t is in seconds and x is in meters; the process to determine the average velocity from t =0 to t =4.0 sec is: A. B. C. Both A and B. D. 8._____ A motorcycle stunt rider rides off the edge of a cliff with a horizontal velocity of 5.0 m/s. Assume air resistance is negligible. The instant before she lands three seconds later, the magnitudes of the horizontal and vertical components of her velocity are: A. 5.0 m/s; 29.8 m/s . B. 5.0 m/s; 0. C. 5.0 m/s; 29.4 m/s. D. 24.4 m/s; 29.4 m/s. 9._____ Consider a particle moving with +v along the +x axis with a negative acceleration. When it reaches its maximum displacement, the velocity will be: A. maximum in a negative direction B. maximum in a positive direction C. zero D. the particle will never reach a maximum displacement, it will continue moving along the +x axis. 10. _____The rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point are ( r ,67.4°). What is r? A. 12 B. 13.0 C. 1.92 D. 4.62

16. [6 pts.] A cheetah is crouched in ambush 20 m to the east of an observer’s blind. At time t =0, the cheetah charges an antelope in a clearing 50 m east of the observer. The cheetah runs along a straight line; the observer quickly calculates the cheetahs’ x coordinate varies with time according to x = (5t 2 + 20) meters. Find the instantaneous velocity of the cheetah when it reaches the antelope. (Assume the antelope remains stationary). 17. [9 pts] A player kicks a football at an angle of 40 ° with the horizontal, with an initial speed of 12 m/s. A second player standing at a distance of 30.0 m from the kicker starts running to meet the ball at the instant it is kicked. What will be the speed of the runner when he catches the ball just before it hits the ground? 18. [9 pts] A surveyor is exploring a cave. He follows a passage 210 m east, then 80 m in a direction 60 ° west of north, then 150 m 45 ° west of south. After a fourth unmeasured displacement he finds himself back where he started. Find the magnitude and direction of this fourth displacement. 19. [8 pts] A batted baseball leaves the bat at an angle of 30.0° above the horizontal and is caught by an outfielder 375 ft from the plate. (Assume the height of the point where it was struck by the bat equals the height of the point where it was caught.) a) how fast was the ball moving when it left the bat? b) how long is the ball in the air? 20. [9 pts] A squirrel moves in a flat field with coordinates given as: r = (2t + t 3 ) i + (6 - t 2 ) j where x and y are measured in m and t in sec . a) Determine the magnitude and direction of the velocity at t = 2.0 sec. b) Determine the magnitude and direction of the acceleration at t = 2.0 sec. c) Determine the magnitude and direction of the displacement at t = 2.0 sec. 21. [8 pts] A model of a helicopter rotor has four blades, each 2.50 m in length from the central shaft to the blade tip and is rotated in a wind tunnel at 1800 rpm. It if started from rest and reached this maximum speed in 15 sec, what is the magnitude of the total acceleration of a blade tip? BONUS [5pts]: Suppose the acceleration due to gravity were only 2.0 m/s 2 instead of 9.8 m/s 2 . Estimate the maximum height of a window from which you would care to jump to a concrete sidewalk below if for g = 9.8 m/s 2 , you would be willing to jump from a height of 4.0 m, which is the typical height of a first-story window?