Answer:
250 m
Explanation:
In projectile, range is given as;
R = (v²sin 2θ)/g
We are given θ = 45°
Thus range of shell is;
R = (v²sin (2 × 45))/g
R = v²/g
Now, distance for the shell to hit the car will be; 150 + 14.14t
This will be equal to the range of shell;
150 + 14.14t = v²/g
Where t is time of flight
Now, time of flight is given by;
t = (2vsin θ)/g
t = (2v sin 45)/g
In surf form, we have;
t = (2v/(g√2))
Simplifying further gives;
t = (v√2)/g
Plugging this value of t into the distance equation gives;
150 + 14.14(v√2)/g = v²/g
Assuming g is 10 m/s², we have;
150 + 14.14(v√2)/10 = v²/10
Multiply through by 10 to get;
1500 + 14.14(v√2) = v²
v² - 20v - 1500 = 0
From quadratic equation calculator, we have; v = 50 m/s
Thus, t = (50√2)/g
t = (50√2)/10
t = 5√2
Plugging this into the distance equation gives;
Distance = 150 + 14.14(5√2) = 250 m
