posted by Anne on .
1) A fish jumps out of the water with a speed of 6.36 m/s. If the fish is in a stream with water speed = to 1.5 m/s, how high can the fish jump if it leaves the water traveling vertically upwards relative to the earth?
2)A ball is thrown by someone on a train moving at 10 m/s on a horizontal track with a path that they judge to be 60 degrees with the horizontal and to be in line with the track. Someone on the ground nearby observes the ball to rise vertically. How high does it rise?
The horizontal velocity component has nothing to do with how high either object goes. Just solve the vertical problems once you find the vertical speed.
a = -g = -9.8 m/s^2
v = Vo - 9.8 t
h = Vo t - 4.9 t^2
at the top, v = 0 so
t = Vo/9.8 at the top
h = (1/2) Vo^2/9.8 = Vo^2/ 19.6
so for problem 1
the horizontal component of speed = 1.5 = 6.36 cos A where A is the angle it leaves the water at.
so A = cos^-1 (1.5/3.6) = 65.4 degrees
so the vertical component of speed is
Vo = 6.36 sin 65.4 = 5.78 m/s
use that to get h
for problem 2
call the speed of the ball S
the horizontal component of velocity is:
10 = S cos 60
S =20 m/s
so the vertical component of S is
Vo = 20 sin 60 = 17.3 m/s
so the vertical component of S