Consider a projectile launched at a height h feet above the ground and at an angle ? with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations x = t(v0 cos(?)) and y = h + (v0 sin ?)t - 16t2. Let h=6, v0=63.25, and ?=0.79. Find the maximum height of the projectile. (Round your answers to two decimal places.)

A 26-pound weight stretches a certain spring 2 feet when the weight and spring are placed in a fluid that resists motion with a force equal to four times the speed. If the weight is stopped at the equilibrium position and then given a velocity of 5 ft / s, find the equation of motion. The DE that models this phenomenon is y "+ Xy '+ (p/l)y = 0, where X is the resistance force of the medium, p is the weight and l the stretch it produces in the spring.

The velocity of a particle is given by v = 39t2-93t+ 47, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 3 seconds of motion and evaluate the velocity when a is zero. Make the plots and then answer the questions. Questions: When t = 0.5 s, V = 10.25 m/s, a= -54 m/s² When t = 1.3 s, V= -7.99 m/s, a = 8.4 m/s² When t = 2.3 s, V= 39.41 m/s, a = 86.64 m/s² When a = 0, V= i 58.25 m/s

Since you are studying mechanics, you decide to consider what Isaac Newton learned by sitting under an apple tree. Fortunately, you decide to wear a helmet, so you may be more practical than Newton was when an apple fell on his head. And you're in luck, an apple (ma = 0.3 kg) falls vertically from the tree and strikes your helmet with a velocity, V₁ = 5 m/sec. The apple then bounces off your helmet to the left at a velocity V₁ = 2 m/sec and an angle of 40° above the horizontal (see the figure). The contact time between the apple and the helmet is 0.12 seconds. (a) Determine the horizontal and vertical components of the impulse exerted by the helmet on the apple. (b) Determine the vertical component of the average impulsive force exerted by the helmet on the apple. V₂ = 2 m/sec Use COLM principles, starting with governing equations, to earn full credit. V₁ = 5 m/sec