Idk if this is the right place to post this but im in need of help with a gamsat physics question
'a terrorist is cornered down the end of a dead end street with a nuclear power plant behind him. a tank is advancing on him but he knows it will not fire and endanger the power plant. he tries to defend himself with a flame thrower. given that he can get maximum range from the flame thrower when the angle of projection is (theta=45 deg) and that, when fresh, the flame thrower can project liquid at a speed of 40root2 m/s, which of the following is closest to the maximum distance the tank can be from him for the weapon to be at all effective?
A. 50m
B. 100m
C. 200m
D. 300m
Answer is D.
Help pls
So this is a projectile question.
We are given two things, the angle at which the liquid was projected (45) degrees and the initial velocity of the liquid. 40root2 m/s
1st thing you should do is find the vertical and horizontal components of the velocity.
Initial vertical velocity = initial velocity * sin (45)
= 40root2 * 1/root2
= 40 m/s
Initial horizontal velocity = initial velocity * cos (45)
= 40root2 * 1/root2, *Note you already know this because it is a right angled isosceles triangle
Since you have both components of velocity first thing you have to find is the total time it takes to reach x (distance).
using the initial vertical velocity (40m/s) use newton's Constant acceleration formula, v = u+at, substituting -10 m/s^2 for acceleration, v = 0 at top of the flight and u = 40 m/s, and solving for time, you get t = 4 seconds for half of the flight.
Therefore, total time it takes for the flight = 2* t
= 8 seconds for the total time.
Now what we do is use the horizontal component to find the distance the liquid will reach. we know that for the horizontal component x (distance) = (horizontal velocity) * (time)
using this distance = 40 m/s * 8
= 320 meters
hence the maximum distance the tank can be from him for the weapon to be effective is 320m, answer is D as 320m is closest to 300m
I hope it can get through to you somehow, i'm sure there may be easier ways to do this, and my explanation is not the best, a better explanation can be done with the aid of a diagram, i'm not great at diagrams XD