Chapter 3.9, Problem 36E

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 time that the projectile stays in the air is

$r(\theta )=\frac{2{\upsilon }_0}{g}\sin \frac{\pi \theta }{180}=102\sin \frac{\pi \theta }{180}\text{seconds}.$

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