Quadratic Problems - Projectile Motion
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How to solve projectile motion word problems using quadratic equations?
Solving projectile problems with quadratic equations
Example: A projectile is launched from a tower into the air with initial velocity of 48 feet per second. Its height, h, in feet, above the ground is modeled by the function
h = -16t2
t + 64
where t is the time, in seconds, since the projectile was launched and v0
is the initial velocity.
(a) How long is the projectile in the air?
(b) When did it reach its maximum height?
(c) What was its maximum height?
Solving a Projectile Problem Using Quadratics
Example: Larry throws a rock in the air. The height, h, in feet above the ground is given by h = -16t2
+ 123t + 40. How long is the rock in the air?
Example: Ellen kicks a stone off the edge of a tall cliff. The distance, d, between the rock and the ground t seconds after being kicked is d = -16t2
- 6t + 480. How many seconds elapse before the rock is at height of 424 ft above the ground?
Example: A ball is kicked in the air. The height of the ball, d, after t seconds is given by d = -16t2
+ 36t + 9. How long is the ball in the air to the nearest hundredth of a second?
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