Question

a projctile is fired at the angle of 53 degree with the horizontal. the speed of the projectile is 200m/s calculate range (use cos53=0.8,sin53=0.6)

Answer 1

Let's first find the time that the projectile takes to reach its maximum height:

$$v_y=v_0sin\theta-gt,$$ $$0=v_0sin\theta-gt$$ $$t=\dfrac{v_0sin\theta}{g}.$$

Then, we can find the total flight time of the projectile:

$$t_{flight}=2t=\dfrac{2v_0sin\theta}{g}.$$

Finally, we can find the range of the projectile:

$$x=v_0tcos\theta,$$ $$x=v_0\dfrac{2v_0sin\theta}{g}cos\theta=\dfrac{v_0^2sin2\theta}{g},$$ $$x=\dfrac{(200\ \dfrac{m}{s})^2sin2\cdot53^{\circ}}{9.8\ \dfrac{m}{s^2}}=3923.5\ m.$$