Answer:
a. ac = 1844.66 m/s²
b. Fc = 265.63 N
Explanation:
a.
The centripetal acceleration of the ball is given as follows:
ac = v²/r
where,
ac = centripetal acceleration = ?
v = speed of ball = (87 mph)(1 h/ 3600 s)(1609.34 m / 1 mile) = 38.9 m/s
r = radius of path = 82 cm = 0.82 m
Therefore,
ac = (38.9 m/s)²/0.82 m
<u>ac = 1844.66 m/s²</u>
<u></u>
b.
The centripetal force is given as:
Fc = (m)(ac)
Fc = (0.144 kg)(1844.66 m/s²)
<u>Fc = 265.63 N</u>
Refer to the figure shown below.
The velocity of the child and the velocity of the ship should be added vectorially to find the speed and direction of the child relative to the water surface.
The magnitude of the child's velocity is
v = √(2² + 18²) = 18.11 mph
The direction of the child's speed is
θ = tan⁻¹ (18/2) = tan⁻¹ 9 = 83.7° north of east or counterclockwise from the eastern direction.
Answer:
The magnitude is 18.1 mph.
The direction is 84° north of east.
Answer:

Explanation:
The kinetic energy of an object is given by
where
is the mass of the object and
is the velocity of the object.
We can set up the following equations with the information given:

For part B, we have the same equation, but kinetic energy is now
.
Therefore:
.
Math is the process of using the given information, along with
all the general stuff that you know, to find the missing information.
With no given information, we have no way to even guess at
an answer.