As provided in the question, heat supplying natural gas furnace operates at 60% efficiency. It means that out of 100 units of heat energy produced by the furnace, only 60 units of heat can be transferred.
Thereby as the demand of the heat energy is 120 MBtu, amount of gas that needs to be purchased equals-
∴ 60% of (cubic metres of gas that needs to be purchased) = 120 MBtu
⇒ (60/100) * gas = 120
⇒ Gas= 120*100/60
∴ Cubic metres of gas that needs to be purchased= 200MBtu
The solution procedure can be found in the attachment below.
The Range is the horizontal distance traveled by a projectile. This diatance is given mathematically by Vo cos(theta) t. Where t is the total time of flight of the projectile in air. It is the time taken for the projectile to go from starting point to finish point. This solution assumes the projectile finishes uts motion on the same horizontal level as the starting point and as a result the vertical displacement is zero (no change in height).
In the solution as can be found below, the expression to calculate the range for any launch angle theta was first derived and then the required angles calculated from the equation by substituting the values of the the given quantities.