Chapter 3.9, Problem 35E

Problems 35–37 investigate the motion of a projectile shot from a cannon. The fixed parameters are the acceleration of gravity, g = 9.8 m∕sec², and the muzzle velocity, υ₀ = 500 m∕sec, at which the projectile leaves the cannon. The angle θ, in degrees, between the muzzle of the cannon and the ground can vary.

The range of the projectile is

$f(\theta )=\frac{v_0^2}{g}\sin \frac{\pi \theta }{90}wq=25,510\sin \frac{\pi \theta }{90}\text{meters}.$

1. (a) Find the range with θ = 20°.
2. (b) Find a linear function of θ that approximates the range for angles near 20°.
3. (c) Find the range and its approximation from part (b) for 21°.