Answer:
962.14m/s
Explanation:
Data obtained from the question include:
m (mass) = 2.8x10^3 kg
P (power) = 30 kW = 30 x 1000 = 30000W
V (velocity) =?
t (time) = 1 day
There are 24 hours in a day.
t (time) = 1 day = 24 hours
We need to covert 24 hours to seconds. This is illustrated below:
There are 60 minutes in 1 hour and 60 seconds in 1 minutes.
Therefore, 24hours = 24 x 60 x 60 = 86400 seconds.
t (time) = 1 day = 24 hours = 86400 seconds
Power is related to velocity according to equation:
Power = force x Velocity
P = F x v (1)
Recall Force (F) = Mass (m) x a (acceleration) i.e F = ma
Substituting the value of F into equation 1, we have:
P = F x v
P = ma x v
P = m x a x v (2)
But: acceleration (a) = Velocity(v)/time(t) i.e a = v/t
Substituting the value of a into equation 2, have:
P = m x a x v
P = m x v/t x v
P = (m x v^2)/ t
Now, with this equation
P = (m x v^2)/ t, we can obtain the speed of the spaceship as follow:
P = (m x v^2)/ t
30000 = (2.8x10^3 x v^2) /86400
Cross multiply to express in linear form
2.8x10^3 x v^2 = 30000 x 86400
Divide both side by 2.8x10^3
v^2 = (30000 x 86400)/ 2.8x10^3
v^2 = 925714.2857
Take the square root of both side
v = √(925714.2857)
v = 962.14m/s
Therefore, the speed of the spaceship is 962.14m/s
