Question

a projectile launched at an angle of 26° does not travel as far as a projectile launched at an angle of 35° if all other parameters are held constant. why is this? it does not have as much velocity, so it cannot travel as far. it does not remain in the air for as long. therefore, it cannot travel as far before hitting the ground. gravity acts more strongly on projectiles launched at lower angles. all of these are true.

Explanation:

The range formula for a projectile is \(R=\frac{v^{2}\sin2\theta}{g}\). The time of flight formula is \(T = \frac{2v\sin\theta}{g}\). When \(\theta = 26^{\circ}\), \(\sin2\theta=\sin52^{\circ}\approx0.788\) and \(\sin\theta=\sin26^{\circ}\approx0.438\). When \(\theta = 35^{\circ}\), \(\sin2\theta=\sin70^{\circ}\approx0.940\) and \(\sin\theta=\sin35^{\circ}\approx0.574\). Since all other parameters (\(v\), \(g\)) are constant, a lower - angle projectile (\(26^{\circ}\)) has a shorter time of flight (\(T\propto\sin\theta\)) and a shorter range (\(R\propto\sin2\theta\)). Gravity (\(g\)) is constant for both projectiles.

Answer:

B. It does not remain in the air for as long. Therefore, it cannot travel as far before hitting the ground.