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 ]
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Answer:
Your zenith is 43 N of 90 deg (equator)
Thus, your zenith is 90 - 43 = 47 deg
(At the N pole your zenith would be 0 deg from the N pole)
Answer:
0.9 N
Explanation:
The force exerted on an object is related to its change in momentum by:

where
F is the force exerted
is the change in momentum
is the time interval
The change in momentum can be rewritten as

where
m is the mass
u is the initial velocity
v is the final velocity
So the formula can be rewritten as

In this problem we have:
is the mass rate
is the initial velocity
is the final velocity
Therefore, the force exerted by the hail on the roof is:

Answer:
1%
Explanation:
Percent error can be found by dividing the absolute error (difference between measure and actual value) by the actual value, then multiplying by 100.

The measured value is 2.02 meters and the actual value is 2.00 meters.


First, evaluate the fraction. Subtract 2.00 from 2.02

Next, divide 0.02 by 2.00

Finally, multiply 0.01 and 100.

The percent error is 1%.