A boat is traveling at a speed of 36 km/h. It has to travel a distance of 210 km. How long will it take?
2 answers:
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A) Zero
The motion of the shot is a projectile's motion: this means that there is only one force acting on the projectile, which is gravity. However, gravity only acts in the vertical direction: so, there are no forces acting in the horizontal direction. Therefore, the x-component of the acceleration is zero.
B) -9.8 m/s^2
The vertical acceleration is given by the only force acting in the vertical direction, which is gravity:
where m is the projectile's mass and g is the gravitational acceleration. Therefore, the y-component of the shot's acceleration is equal to the acceleration due to gravity:
where the negative sign means it points downward.
C) 7.6 m/s
The x-component of the shot's velocity is given by:
where
is the initial velocity
is the angle of the shot
Substituting into the equation, we find
D) 9.3 m/s
The y-component of the shot's velocity is given by:
where
is the initial velocity
is the angle of the shot
Substituting into the equation, we find
E) 7.6 m/s
We said at point A) that the acceleration along the x-direction is zero: therefore, the velocity along the x-direction does not change, so the x-component of the velocity at the end of the trajectory is equal to the x-velocity at the beginning:
F) -11.1 m/s
The y-component of the velocity at time t is given by:
where
is the initial y-velocity
a = g = -9.8 m/s^2 is the vertical acceleration
t is the time
Since the total time of the motion is t=2.08 s, we can substitute this value into the equation, and we find:
where the negative sign means the vertical velocity is now downward.