Question

Q.1. An artillery shell is launched at an angle of 50˚ and a velocity of 850 m/s. It hits a target on a hilltop at a height of 2000 m. Find (a) the x and y components of the shell’s initial velocity, (b) the total time of flight for the ball, and (c) the horizontal distance to the target?

Q.2. A plane drops a box of supplies while traveling at a horizontal velocity of 50 m/s. If the box lands on the ground after 76 s, find (a) the height Y from which plane dropped the box and (b) the horizontal distance X traveled by the box after being dropped. 

Q.3. A 10.00-kg block is sliding down a ramp making an angle of 50˚ with the ground. Find (a) normal force applied by the ramp on the box, and (b) the force of friction between the block and the ramp (µ_k = 0.25, µ_s = 0.40), and (c) the acceleration of the box down the ramp.

Q.4. (a) Find the tension T in a cable holding a 76 x 100 kg elevator that is cruising upward at a velocity of 5 m/s. Brakes are then applied such that the elevator comes to a stop in 4s. Find (b) the acceleration after the brakes are applied and (c) the tension in the cable during the braking period.

Note: Figures and free-body vector diagrams must be part of solutions to the problems. Final answers to problems would not accepted in the absence of necessary steps.

Answer 1

1) a)

$$v_x=850\cos{50}=546\frac{m}{s}\\v_y=850\sin{50}=651\frac{m}{s}$$

b)

$$2000=850\sin{50}t-0.5(9.8)t^2\\t=3.15\ s$$

c)

$$x=850\cos{50}\cdot3.15=1720\ m$$

2) a)

$$Y=0.5(9.8)(76)^2=28300\ m$$

b)

$$X=50(76)=3800\ m$$

3) a)

$$N=(10)(9.8)\cos{50}=63\ N$$

b)

$$F_f=0.25(63)=15.75\ N$$

c)

$$10a=(10)(9.8)\sin{50}-15.75\\a=5.93\frac{m}{s^2}$$

4) a)

$$T=(7600)(9.8)=74480\ N$$

b)

$$a=\frac{5}{4}=1.25\frac{m}{s^2}$$

c)

$$T=(7600)(9.8-1.25)=64980\ N$$