Very Confusion (Multiple Choice) (1 Viewer)

[untouchablecuz]

Napoleon attacked Moscow in 1812 with his cannon firing a shot at an elevation angle of 40°. Napoleon then decided to fire a second shot at the same speed but at an elevation angle of 50°.

Which of the following observations would Napoleon expect to be true about the second shot when compared with the first?

(A) Longer range
(B) Shorter range
(C) Longer time of flight
(D) Shorter time of flight

HSC 2005, Q5

first cannon: x(1) = Vtcos40 = Vt(0.77)

second cannon: x(2) = Vtcos50 = Vt(0.64)

hence by comparison,

x1 > x2, hence B

but the answers say C (it may also be correct, but that means that there are two answers)

someone help? please

 

[annabackwards]

I remember doing this quetions and getting confused too.

If you find the total time of flight for each the differeny shots, they're different for the 2 shots. Sub those values of t so sub it back into the equation for range for each shot and you'll get the same answer.

Hence, the range is the same but the times of flight are different

 

[kaz1]

The ranges are the same but the higher the angle the longer the time of flight.

 

[darkchild69]

Using following equations:

Time of flight = 2*u*Sin(theta)/g

As theta moves from 0-90 Time of flight increases to a maximum --> 50 degrees has a longer time of flight


Range = u^2Sin(2theta)/g

As theta moves from 0-45 Range increases to a maximum, as it falls from 45-90 it falls to zero.

Also remember that Sin(90+theta) = Sin(90-theta)

So, if the deviation from the launch angle of 45degrees is the same (plus or minus) then the range will be equal. [Keep in mind it is Sin(2theta) and Sin(45*2) = Sin(90)]

i.e., 40 and 50 degrees are 5 degrees either side of 45 so will be the same range