R

vo = 65.0 m/s

125 m

UNIVERSITI TUNKU ABDUL RAHMAN CentreCourseYear/ TrimesterSession

: Centre for Foundation Studies (CFS): Foundation in Science: Year 1 / Trimester 1: 201205

Unit CodeUnit TitleLecturer

: FHSC1014: Mechanics: Mr. Lim Min Leong Mr. Foo Seng Teek Ms. Ng Wei Ling Mr. Woon Fook Sim Ms. Nurfadzilah

Additional Tutorial 3: Projectile motion + Laws of motion 1.

A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 65.0 m/s at an angle of 37.0° with the horizontal.(a) Determine the time taken by the projectile to hit the ground level.(b) Determine the range R of the projectile as measured from the base of the cliff.(c) Find the maximum height above the cliff top reach by the projectile.

[Answer: (a) 10.42 s; (b) 540.9 m; (c) 78.0 m]

2. An airplane with a speed of 100 m/s is climbing upward at an angle of 50.0° with respect to the horizontal. When the plane’s altitude is 900 m, the pilot releases a package.(a) Calculate the distance along the ground, measured from a point directly

beneath the point of release, to where the package hits the earth.(b) Determine the angle of the velocity vector of the package just before impact

with the ground.[Answer: (a) 1.51 km; (b) –67.3°]

3.

A 2.00 m tall basketball player is standing on the floor 10.0 m from the basket, as in figure. If he shoots the ball at a 40.0° angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 m.

[Answer: 10.7 m/s]

1

7.20 m

1.55 m40.0°

4.

A basketball of mass, m = 0.600 kg is shot with an initial velocity of vo at the angle of 40.0° above the horizontal undergoes a projectile motion. Neglecting the air resistance, if the basketball is to shoot into the basket which is fixed at horizontal distance of 7.20 m ahead and 1.55 m above the position of the basketball, find (a) the initial speed, vo, (b) the velocity (magnitude and direction) of the basketball, v, at the rim.

[Answer: (a) 9.82 m s–1; (b) 8.12 m s–1, 22.2°]

5. A soccer player kicks the ball toward a goal that is 16.8 m in front of him. The ball leaves his foot at a speed of 16.0 m/s and an angle of 28.0° above the ground. Find the speed of the ball when the goalie catches it in front of the net.

[Answer: 14.7 m/s]

6. A stunt driver wants to make his car jump over eight cars parked side by side below a horizontal ramp as shown in figure below.

(a) With what minimum speed must he drive off the horizontal ramp? The vertical height of the ramp is 1.5 m above the cars, and the horizontal distance he must clear is 20 m.

(b) If the ramp is now tilted upward, so that “takeoff angle” is 10° above the horizontal, what is the new minimum speed?

[Answer: (a) 36.2 m s–1; (b) 20.1 m s–1]

7. The distance between two telephone poles is 50.0 m. When a 1.00 kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. Draw a free-body diagram of the bird. How much tension does the bird produce in the wire? Ignore the weight of the wire.

[Answer: 614 N]

8. A worker stands still on a roof sloped at an angle of 31° above the horizontal. He is prevented from slipping by a static frictional force of 420 N. Find the mass of the worker.

[Answer: 83 kg]

2

9. A block is pressed against a vertical wall by a force P⃗ , as the drawing shows. This force can either push the block upward at a constant velocity or allow it to slide downward at a constant velocity. The magnitude of the force is different in the two cases, while the directional angle is the same. Kinetic friction exists between the block and the wall, and the coefficient of kinetic friction is 0.250. The

weight of the block is 39.0 N, and the directional angle for the force P⃗

is = 30.0°. Determine the magnitude of when the block slides(a) up the wall and(b) down the wall.

[Answer: (a) 52.6 N; (b) 39.4 N]

10. A 3.0 kg block is at rest on a horizontal floor. If you push horizontally on the 3.0 kg block with a force of 12.0 N, it just starts to move.(a) What is the coefficient of static friction? (b) A 7.0 kg block is stacked on top of the 3.0 kg block. What is the magnitude F

of the force, acting horizontally on the 3.0 kg block that is required to make the two blocks start to move?

[Answer: (a) 0.41; (b) 40 N]

11.

Two blocks are sliding to the right across a horizontal surface, as the drawing shows. In Case A the mass of each block is 3.0 kg. In Case B the mass of block 1 (the block behind) is 6.0 kg, and the mass of block 2 is 3.0 kg. No frictional force acts on block 1 in either Case A or Case B. However, a kinetic frictional force of 5.8 N does act on block 2 in both cases and opposes the motion. For both Case A and Case B determine (a) the magnitude of the forces with which the blocks push against each other and (b) the magnitude of the acceleration of the blocks.

[Answer: (a) 2.9 N, 3.9 N; (b) 0.97 m/s2, 0.64 m/s2]

12. Two blocks of masses m1 and m2 (m1 > m2) are placed on a frictionless table in contact with each other. A horizontal force of magnitude F is applied to the block of mass m1 as shown in the figure. (a) If P is the magnitude of the contact force between the blocks, draw the free-

body diagrams for each block. (b) What is the net force on the system consisting of both blocks? (c) What is the net force acting on m1? (d) What is the net force acting on m2? (e) Write the x-component of Newton’s second law for each block. (f) Solve the resulting system of two equations and two unknowns, expressing the

acceleration a and contact force P in terms of the masses and force.(g) How would the answers change if the force had been applied to m2 instead? Is

the contact force larger, smaller or the same in this case? Why?

3

[Answer: (b) F; (c) F – P; (d) P; (e) m1a, m2a; (f) a= F

(m1+m2 ) , P=( m2

m1+m2)F

]

4