I need help with projectile motion of PreCalc the 5 question

I need help with projectile motion of PreCalc, (the 5 questions posted)

Ch a pter 6 Pro j ect Projectile Motion Parametric equations are equations that represent two variables in terms of athird variable, called the parameter. In this project, you will use parametric equations to model the path of a projectile.These parametric equations represent position x and position y in terms of time t. For any time t, the horizontal position x() and vertical position y( of a projectile (ignoring air resistance) launched at ground level is given by the parametric equations t) va cos 80t (vo sin 00t 16t In these equations, is the angle with the horizontal and vo is the initial velocity in feet per second, as indicated in Figure l Figure 1 Set your graphing utility to parametric and degree modes, and use the viewing window shown in Figure 2. Let v 88 feet per second and 6- 20, and graph the parametric equations Tstep Xnin t) (88 cos 20°)r y()- (88 sin 20°)t 1613. YMax Use the zoom and trace features of your graphing utility to (a) find the maximum height attained by the projectile, (b) find the time at which the maximum height Figure 2 occurs, (c) determine the length of time that the projectile is in the air, and (d) determine the range of the projectile Questions for Further Exploration 5. Eliminate t from the parametric equations x()- (va cos and (va sin 6) 16t2 I. Verify algebraically the range of the projectile by solving the equation (88 sin 20°)r 16t 0 for t by solving for t in the first equation and substituting and then evaluating x(t) at this t-value this value into the equation for y. Show in this Use a graphing utility to find the maximum height case that the height of the projectile is given by the and range of the projectile when 6 300 and va 132 feet per second. 16 sec 20 3. Let vo 60 feet per second. Find the range for the y (tan angles 20°, 30°, 40°, 500, and 60°. In general what angle should you use to produce the maximum Use this equation to find the angle 6 corresponding range? to a range of 200 feet and initial velocity of vo- 80 feet per second. 4. What is the relationship between the time the projectile reaches its maximum height and the time it takes for the projectile to return to the ground? Explain

Solution

1. (88sin20)t-16t^2=0

30.1 t -16t^2=0

t(30.1 -16t)=0

t=0 , t=30.1/16

t=0 , t=1.88

x(t)=(88 cos 20 )*0 =82.7feet

x(t)=(88cos 20)1.88=155.5 feet