A ball is thrown straight upward and returns to the thrower\'s hand after 3.10 s

Question

A ball is thrown straight upward and returns to the thrower's hand after 3.10 s in the air. A second ball thrown at an angle of 45.0° with the horizontal reaches the same maximum height as the first ball.

(a) At what speed was the first ball thrown?

______m/s

(b) At what speed was the second ball thrown?

_______m/s

A hunter wishes to cross a river that is 1.8 km wide and flows with a speed of 5.0 km/h parallel to its banks. The hunter uses a small powerboat that moves at a maximum speed of 11 km/h with respect to the water. What is the minimum time necessary for crossing?

__________min

Explanation / Answer

a) from the relation

y = ut+1/2at^2

here y = 0 ,t = 3.1 s

a = -9.8 m/s^2

ut = 1/2gt^2

u = 1/2g*t

u = 1/2*9.8*3.1 = 15.19 m/s

b) maximu height in first case

h = u^2/2g = 15.19^2/2*9.8 = 11.8 m

in the second case

h max = u^2sin^2(45)/2g

11.8 = u^2sin^2(45)/2*9.8

u^2 = 462.56

u = sqrt(462.56)

u = 21.51 m/s

2) actual velocity of boat with respect to the earth

v = sqrt(5^2+11^2) = 12.08 km/h

tan(theta) = 5/11

theta = tan^1(5/11) = 24.4 degrees

path length r = 1.8/cos(24.4) = 1.98 km

time t = r/v

t = 1.98/12.08 = 0.164 hr

t = 0.164*60 = 9.84 min

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