6. A pitcher throws a ball toward home plate 18.39 meters away. If the ball is traveling at a constant 40.0 m/s, how long does i
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a) Time of flight: 22.6 s
To calculate the time it takes for the cargo to reach the ground, we just consider the vertical motion of the cargo.
The vertical position at time t is given by
where
h = 2.5 km = 2500 m is the initial height
is the initial vertical velocity of the cargo
g = 9.8 m/s^2 is the acceleration of gravity
The cargo reaches the ground when
So substituting it into the equation and solving for t, we find the time of flight of the cargo:
b) 7.5 km
The range travelled by the cargo can be calculated by considering its horizontal motion only. In fact, the horizontal motion is a uniform motion, with constant velocity equal to the initial velocity of the jet:
So the horizontal distance travelled is
And if we substitute the time of flight,
t = 22.6 s
We find the range of the cargo: