A 0.87 kg projectile is fired into the air from the top of a 8.52 m cliff above a valley. Its initial velocity is 9.1 m/s at 49◦
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By using first and third equation of motion, the number of revolutions the tire makes during this motion is 43 rev.
ANGULAR MOTION
Since the car accelerate from rest, initial velocity will be zero.
Given that a car accelerates uniformly from rest and reaches a speed of 24.3 m/s in 9.1 s. The following are the given parameters
- Initial velocity U = 0
- Final velocity V = 24.3 m/s
- Time t = 9.1 s
If the diameter of a tire is 80.2 cm, to find the number of revolutions the tire makes during this motion, we must first calculate the distance travelled by the car by using first and third equation of motion of the car.
First equation
V = U + at
Substitute all necessary parameters into the equation.
24.3 = 0 + 9.1a
a = 24.3/9.1
a = 2.67 m/
Third Equation of motion
Substitute all the necessary parameters
= 0 + 2 x 2.67 x S
590.49 = 5.34S
S = 590.49 / 5.34
S = 110.58 m.
Given that the diameter of a tire is 80.2 cm,
the radius (r) will be 80.2/2 = 40.1 cm
convert it to meter
r = 40.1/100 = 0.401 m
The Circumference of the tire = 2r
Circumference = 2 x 3.143 x 0.401
Circumference = 2.52 m
Assuming no slipping, number of revolutions = 110.58/2.52
Number of revolutions = 43.89 rev.
Number of revolutions = 43 rev.
Therefore, the number of revolutions the tire makes during this motion is 43 rev.
Learn more about circular motion here: brainly.com/question/6860269
Jane's mechanical energy at any time is
where
is the potential energy, while 
is the kinetic energy.
Initially, Jane is on the ground, so the altitude is h=0 and the potential energy is zero: U=0. She's running with speed v, so she has kinetic energy only:
Then she grabs the vine, and when she reaches the maximum height h, her speed is zero: v=0, and so the kinetic energy becomes zero: K=0. So now her mechanical energy is just potential energy:
But E must be conserved, so the initial kinetic energy must be equal to the final potential energy:
from which we can find h, the maximum height Jane can reach:
where
Initially, Jane is on the ground, so the altitude is h=0 and the potential energy is zero: U=0. She's running with speed v, so she has kinetic energy only:
Then she grabs the vine, and when she reaches the maximum height h, her speed is zero: v=0, and so the kinetic energy becomes zero: K=0. So now her mechanical energy is just potential energy:
But E must be conserved, so the initial kinetic energy must be equal to the final potential energy:
from which we can find h, the maximum height Jane can reach: