Projectile motion and parametric equations

Eliminate the parameter. Convert the parametric equation to rectangular. x= 2+4t and y=-1+6t

• y=(3/2)x - 4
• t=(x-2)/4
• y=x - 4
• y= (2/3)x + 4

Eliminate the parameter. Convert the parametric equation to rectangular. x= t - 1 and y=t² - 2

• y=(x+1)² - 2
• t=x - 1
• x=t - 1
• y=t - 2

Tags

CCSS.HSF-BF.B.4A

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

• 13.5 f/s

• 14.1 f/s

• 18.6 f/s

• 33.1 f/s

The height of an object can be modeled by the formula h(t) = -16t² + 70t + 95, where h(t) is in feet after t seconds.

What is the height of the object after 5 seconds?

• 95 feet

• 45 feet

• 70 feet

• 171.56 feet

An NFL punter at the 20 yard line kicks a football downfield with an initial velocity of 75 ft/sec at an angle of 66⁰. The ball leaves his foot at a height of 3 feet.

Model the scenario using parametric equations.

• x = (20cos(66⁰))t; y=-16t² + (20sin(66⁰)t + 75

• x = (20cos(66⁰))t; y=-16t² + (20sin(66⁰)t + 3

• x = (75cos(66⁰))t; y=-16t² + (75sin(66⁰)t + 20

• x = (75cos(66⁰))t; y=-16t² + (75sin(66⁰)t + 3

An NFL punter at the 20 yard line kicks a football downfield with an initial velocity of 75 ft/sec at an angle of 66⁰. The ball leaves his foot at a height of 3 feet.

How high will the ball be when it reaches the crossbar of the goalposts, which are 25 yards (75 feet) away from the kicker?

• -81.516

• 74.734

• 28.236

• 25

Mr. Salaam hits a baseball to Mr. Shakin at 3 ft above the ground with an initial speed of 150 ft/sec and at angle of 18 degrees with the horizontal.

Model the x component with a parametric equation.

• x = (3 cos 18) t

• x = (150 cos 18)t

• x = (150 cos 18)

• x = (150 cos 3)t

Mr. Salaam hits a baseball to Mr. Shakin at 3 ft above the ground with an initial speed of 150 ft/sec and at angle of 18 degrees with the horizontal.

Model the y component with a parametric equation.

• y = -16t²+(150 sin 18)t

• y = -16t²+(150 sin 3)t+18

• y = -16t²+(150 sin 18)t+3

• y = 16t²+(150 sin 3)+18

Mr. Salaam hits a baseball to Mr. Shakin at 3 ft above the ground with an initial speed of 150 ft/sec and at angle of 18 degrees with the horizontal.

How far away is the ball from Mr. Salaam

after 1.5 seconds?

• 180.988 feet

• 36.529 feet

• 46.353 feet

• 213.988 feet

Mr. Salaam hits a baseball to Mr. Shakin at 3 ft above the ground with an initial speed of 150 ft/sec and at angle of 18 degrees with the horizontal.

How long does it take the ball to

travel 100 feet horizontally?

• 0.206 sec

• 0.701 sec

• 0.634 sec

• 2.157 sec