A river flows due east at 1.50 m/s. A boat crosses the river from the south shor

Question

A river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.0 m/s due north relative to the water. A) What is the velocity of the boat relative to the shore? B) If the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north shore? The brakes of a car moving at 50 km/hr are suddenly applied, and the car a complete stop in 4 s. What was its acceleration (assumed constant) in (km/ and b) in m/s^2?

Explanation / Answer

25. v_river = 1.50 m/s i

v_boat wrt river = 10 m/s j

v_boat wrt river = v_boat - v_river

v_boat = 1.50i + 10j

magnitude = sqrt(1.50^2 + 10^2) = 10.11 m/s

direction = tan^-1(10/1.50) = 81.5 deg

veloccity = 10.11 m/s 81.5 deg with shore (north of east)

(B) 300 m is along south to north

time taken to reach the shore = 300 / 10 = 30 sec

displacment along the shore = 30 x 1.5 = 45 m .......Ans

26). initial velocity, v0 = 50 km/hr = 50 x 1000 m / 3600 s

v0 = 13.89 m/s

final velocity, vf = 0

Applying vf = v0 + a t

0 = 13.89 + 4a

a = - 3.47 m/s^2 .......Ans(in m/s^2)
(minus sign because it is deceleartion, magnitude will be 3.47 m/s^2)

in km/h^2 : 0 = 50 + (4/3600) a

a = 45000 km/h^2 .....Ans

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