Final answer:
The equation for the energy possessed by an object of mass m kg travelling at a height h m with a velocity v m/s is e = mv²/2 + mgh joules. To express v in terms of the other variables, rearrange the equation as v = sqrt(2(e - mgh)/m). Given the energy of a 20 kg mass at a height of 15 m is 4900 joules and g = 9.8 m/s², substitute these values into the equation and solve for v. The mass is travelling at a speed of approximately 44.72 m/s.
Step-by-step explanation:
The energy of an object of mass m kg travelling at a height h m with a velocity v m/s is given by the equation e = mv²/2 + mgh joules. To express v in terms of the other variables, we can rearrange the equation as v = sqrt(2(e - mgh)/m).
Given that the energy of a 20 kg mass at a height of 15 m is 4900 joules and g = 9.8 m/s², we can substitute these values into the equation and solve for v.
By substituting the known values, we get 4900 = (20)v²/2 + (20)(9.8)(15). Simplifying this equation, we find that v² = (4900 - 29400)/20. Taking the square root of both sides, we obtain v = sqrt(2000). Therefore, the mass is travelling at a speed of approximately 44.72 m/s.