Q. A ball is thrown at an angle of 45 degrees with an initial speed of 28 m/s. What is the vertical component of the velocity at the peak of its trajectory?
A.0 m/s
B.14 m/s
C.20 m/s
D.28 m/s
Solution
At the peak, the vertical component of velocity is 0 m/s.
Q. A ball is thrown horizontally from the top of a cliff 45 m high. How far from the base of the cliff will it land if it is thrown with a speed of 10 m/s?
A.20 m
B.30 m
C.40 m
D.50 m
Solution
Time to fall = sqrt(2h/g) = sqrt(2*45/9.8) ≈ 3.03 s. Horizontal distance = speed * time = 10 * 3.03 ≈ 30.3 m, approximately 30 m.
Q. A ball is thrown horizontally from the top of a cliff 80 m high. How far from the base of the cliff will it land? (Assume g = 10 m/s² and horizontal speed = 20 m/s)
A.20 m
B.40 m
C.60 m
D.80 m
Solution
Time to fall = √(2h/g) = √(2*80/10) = 4 s. Horizontal distance = speed * time = 20 m/s * 4 s = 80 m.
Q. A ball is thrown horizontally from the top of a cliff 80 m high. How far from the base of the cliff will it land? (Assume g = 10 m/s² and initial horizontal speed = 20 m/s)
A.40 m
B.60 m
C.80 m
D.100 m
Solution
Time to fall = √(2h/g) = √(2*80/10) = 4 s. Horizontal distance = speed * time = 20 * 4 = 80 m.
Q. A ball is thrown horizontally from the top of a cliff with a speed of 15 m/s. If the cliff is 45 m high, how far from the base of the cliff will the ball land?
A.30 m
B.45 m
C.60 m
D.75 m
Solution
Time to fall = √(2h/g) = √(2*45/10) = 3 s. Horizontal distance = speed * time = 15 m/s * 3 s = 45 m.
Q. A ball is thrown vertically upwards with a speed of 30 m/s. How high will it rise before coming to rest momentarily?
A.45 m
B.30 m
C.60 m
D.75 m
Solution
Using the equation v² = u² + 2as, where v = 0, u = 30 m/s, and a = -9.8 m/s² (acceleration due to gravity), we have 0 = (30)² + 2*(-9.8)*s. Solving gives s = 45.92 m, approximately 45 m.
Q. A boat can travel at 10 km/h in still water. If it is moving downstream in a river flowing at 5 km/h, what is the speed of the boat relative to the riverbank?
A.5 km/h
B.10 km/h
C.15 km/h
D.20 km/h
Solution
Speed downstream = Speed of boat + Speed of river = 10 km/h + 5 km/h = 15 km/h.
Q. A boat can travel at 12 km/h in still water. If it is going downstream in a river flowing at 4 km/h, what is the speed of the boat relative to the riverbank?
A.8 km/h
B.12 km/h
C.16 km/h
D.20 km/h
Solution
Speed of boat downstream = Speed of boat + Speed of river = 12 km/h + 4 km/h = 16 km/h.
Q. A boat can travel at 12 km/h in still water. If it is going downstream in a river flowing at 3 km/h, what is the speed of the boat relative to the riverbank?
A.9 km/h
B.12 km/h
C.15 km/h
D.3 km/h
Solution
Speed of boat downstream = Speed of boat + Speed of river = 12 km/h + 3 km/h = 15 km/h.
Q. A boat can travel at 12 km/h in still water. If it is moving downstream in a river flowing at 4 km/h, what is the speed of the boat relative to the riverbank?
A.8 km/h
B.12 km/h
C.16 km/h
D.4 km/h
Solution
Speed of boat relative to riverbank = Speed of boat + Speed of river = 12 km/h + 4 km/h = 16 km/h.
Q. A boat can travel at 15 km/h in still water. If it takes 2 hours to travel upstream and 1.5 hours to travel downstream, what is the speed of the current?
A.2 km/h
B.3 km/h
C.4 km/h
D.5 km/h
Solution
Let speed of current = x. Upstream speed = 15 - x, Downstream speed = 15 + x. (2 hours)(15 - x) = (1.5 hours)(15 + x). Solving gives x = 3 km/h.
