To solve this problem we will apply the concept related to the kinetic energy theorem. Said theorem states that the work done by the net force (sum of all forces) applied to a particle is equal to the change experienced by the kinetic energy of that particle. This is:
Here,
m = mass
v = Velocity
Our values are given as,
Replacing,
Therefore the mechanical energy lost due to friction acting on the runner is 907J
The horizontal range of the missile is b) 176 m
Explanation:
The motion of the missile is a projectile motion, so it consists of two independent motions:
- A uniform motion with constant velocity along the horizontal direction
- A uniformly accelerated motion with constant acceleration (equal to the acceleration of gravity) in the vertical-downward direction
To find the time of flight of the missile, we study the vertical motion. We can use the following suvat equation:
where:
s = 75 m is the vertical displacement of the missile (the height of the building)
is the initial vertical velocity (the missile is thrown horizontally)
t is the time of flight
is the acceleration of gravity
Solving for t, we find the time of flight:
This means that the missile takes 3.91 s to reach the ground.
Now we study the horizontal motion: the missile moves with a constant horizontal velocity of
Therefore, the distance covered in a time t is
and by substituting t = 3.91 s, we find the horizontal range of the missile:
Learn more about projectile motion:
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