W = Fd = 4(2100) = 8400 J
So the answer is A) 8400 J
I was just rewriting my notes on the work lesson I did in class today, so I saw this question at the perfect time!! :)
Hope it helps!! :)
it is just a matter of integration and using initial conditions since in general dv/dt = a it implies v = integral a dt
v(t)_x = integral a_{x}(t) dt = alpha t^3/3 + c the integration constant c can be found out since we know v(t)_x at t =0 is v_{0x} so substitute this in the equation to get v(t)_x = alpha t^3 / 3 + v_{0x}
similarly v(t)_y = integral a_{y}(t) dt = integral beta - gamma t dt = beta t - gamma t^2 / 2 + c this constant c use at t = 0 v(t)_y = v_{0y} v(t)_y = beta t - gamma t^2 / 2 + v_{0y}
so the velocity vector as a function of time vec{v}(t) in terms of components as[ alpha t^3 / 3 + v_{0x} , beta t - gamma t^2 / 2 + v_{0y} ]
similarly you should integrate to find position vector since dr/dt = v r = integral of v dt
r(t)_x = alpha t^4 / 12 + + v_{0x}t + c let us assume the initial position vector is at origin so x and y initial position vector is zero and hence c = 0 in both cases
r(t)_y = beta t^2/2 - gamma t^3/6 + v_{0y} t + c here c = 0 since it is at 0 when t = 0 we assume
r(t)_vec = [ r(t)_x , r(t)_y ] = [ alpha t^4 / 12 + + v_{0x}t , beta t^2/2 - gamma t^3/6 + v_{0y} t ]
8.16m is the required height, a 5kg stone need to be raised.
One sort of potential energy is gravitational potential energy, which is equal to the product of the object's mass (m), the gravitational acceleration (g), and the object's height (h) as measured in relation to the ground's surface (the body).
We obtain the formula by considering the work done in raising a mass m through a height h.
Work in elevating mass m through height h is equal to force times distance.
The force must be greater than the mass m's weight, hence F = mg.
Work done = mgh = gravitational potential energy
Energy = Mass of the object × gravitational acceleration × height.
Mass of the stone = 5kg
Equating ;
∴ 400 J = 5 kg × 9.8 m/s² × height
Height = 8.16 m
Therefore, 8.16m is the required height.
Learn more about energy here:
brainly.com/question/1242059
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Solution :
Speed of the air craft, 
= 262 m/s
Fuel burns at the rate of, 
= 3.92 kg/s
Rate at which the engine takes in air, 
= 85.9 kg/s
Speed of the exhaust gas that are ejected relative to the aircraft, 
=921 m/s
Therefore, the upward thrust of the jet engine is given by
F = 85.9(921 - 262) + (3.92 x 921)
= 4862635.79 + 3610.32
= 
Therefore thrust of the jet engine is .
