What if I don’t give you the answer
Answer:
v₀ₓ = 63.5 m/s
v₀y = 54.2 m/s
Explanation:
First we find the net launch velocity of projectile. For that purpose, we use the formula of kinetic energy:
K.E = (0.5)(mv₀²)
where,
K.E = initial kinetic energy of projectile = 1430 J
m = mass of projectile = 0.41 kg
v₀ = launch velocity of projectile = ?
Therefore,
1430 J = (0.5)(0.41)v₀²
v₀ = √(6975.6 m²/s²)
v₀ = 83.5 m/s
Now, we find the launching angle, by using formula for maximum height of projectile:
h = v₀² Sin²θ/2g
where,
h = height of projectile = 150 m
g = 9.8 m/s²
θ = launch angle
Therefore,
150 m = (83.5 m/s)²Sin²θ/(2)(9.8 m/s²)
Sin θ = √(0.4216)
θ = Sin⁻¹ (0.6493)
θ = 40.5°
Now, we find the components of launch velocity:
x- component = v₀ₓ = v₀Cosθ = (83.5 m/s) Cos(40.5°)
<u>v₀ₓ = 63.5 m/s</u>
y- component = v₀y = v₀Sinθ = (83.5 m/s) Sin(40.5°)
<u>v₀y = 54.2 m/s</u>
Answer:
78.4 J
Explanation:
The gravitational potential energy of an object is the energy possessed by the object due to its location in the gravitational field.
The change in gravitational potential energy of an object is given by:

where:
m is the mass of the object
is the acceleration due to gravity
is the change in height of the object
For the mass in this problem, we have:
m = 2 kg is the mass
is the change in height
So, its change in gravitational energy is:

Answer:
a) 
b) 
c)
d) 
Explanation:
Given:
- mass of the astronaut,

- vertical displacement of the astronaut,

- acceleration of the astronaut while the lift,

a)
<u>Now the force of lift by the helicopter:</u>
Here the lift force is the resultant of the force of gravity being overcome by the force of helicopter.

where:
force by the helicopter
force of gravity


b)
The gravitational force on the astronaut:



d)
Since the astronaut has been picked from an ocean we assume her initial velocity to be zero, 
using equation of motion:



c)
Hence the kinetic energy:


