Projectile Motion with Parametric Equations

A cannonball is fired from a height of 3 feet, at a 45 degree angle with an initial velocity of 625 feet per second. Write an equation to model the horizontal motion of the cannonball.

•  $y=625\sin\left(45\right)$  

•  $x=625\cos\left(45\right)t$  

•  $x=625\cos\left(45\right)t+3$  

•  $y=625\sin\left(45\right)t+3$  

A cannonball is fired at a 45 degree angle with an initial velocity of 625 feet per second. Find the horizontal distance of the cannonball after 2 seconds.

• 1250

• 441.9

• 883.9

• 328.3

A cannonball is fired from a height of 3 feet, at a 45 degree angle with an initial velocity of 625 feet per second. Write an equation to model the vertical motion of the cannonball.

•  $y=625\sin\left(45\right)$  

•  $y=-16t^2+625\sin\left(45\right)t$  

•  $y=-16t^2+625\sin\left(45\right)t+3$  

•  $y=625\sin\left(45\right)t+3$  

A cannonball is fired from a height of 3 feet, at a 45 degree angle with an initial velocity of 625 feet per second. How long is the cannonball in the air?

• 27.6 seconds

•  13.8 seconds

• 10.3 seconds

• 20.5 seconds

The height of an object can be modeled by the formula $h\left(t\right)=-16t^2+140\sin\left(30\right)t+95$ 
What is the height of the object after 5 seconds?

• 95 feet

• 45 feet

• 70 feet

• 171.56 feet

An NFL kicker at the 20 yard line kicks a footbal downfield with an initial velocity of 75 ft/sec at an angle of 66 degrees. The ball leaves his foor at a height of 3 feet.

Write a set of parametric equations to model the motion of the ball.

• $x=20\cos\left(66\right)t\ \ \ ,\ \ \ \ y=-16t^2+20\sin\left(66\right)t+75$

• $x=75\cos\left(66\right)t\ \ \ ,\ \ \ \ y=-16t^2+75\sin\left(66\right)t+20$

• $x=20\cos\left(66\right)t\ \ \ ,\ \ \ \ y=-16t^2+20\sin\left(66\right)t+3$

• $x=75\cos\left(66\right)t\ \ \ ,\ \ \ \ y=-16t^2+75\sin\left(66\right)t+3$

A ball is thrown horizontally at a height of 2.2 meters at a velocity of 65m/s. How far did the ball travel horizontally when it hit the ground?

• 14.3 m

• 30.55 m

• 65 m

• 43.55

A ball is kicked with a 36 degree angle and a velocity of 23 f/s. Find the horizontal distance of the ball after 1 second.

• 13.5

• 14.1

• 18.6

• 33.1

A model rocket is launched from the roof of a building. Its flight path is modeled by the quadratic function $h\left(t\right)=-16t^2+192\sin\left(90\right)+64$  

What is the height of the rocket after 3 seconds?

• 16 feet

• 208 feet

• 256 feet

• 304 feet

Alex hits the baseball at a 28 degree angle with an initial velocity of 103 feet per second from an initial height of 4 feet. The ball is not caught by the outfielder and hits the ground. How far from home plate does the ball land?

• 282 feet

• 347 feet

• 188 feet

• 226 feet