math
posted by James .
Sam kicks a ball horizontally along a deck that is 5 m
above the ground.
The ball goes off the edge of the deck.
A model for the path of the ball once it leaves the deck is a parabola.
The equation of the parabola is y = ax^2+ bx + c.
The ball hits the ground at a horizontal distance of 3.1 m from the edge of the deck.
Find the values of a, b and c.
SHOW WORKING. STEP BY STEP

If y is the height above the ground,
y = 5 when x = 0, so
a*0^2 + b*0 + c = 5,
so c = 5
When x = 0, the slope of the trajectory (path) is zero, so
dy/dx = 2ax + b = 0 at x = 0, so b = 0
When x = 3.1, y = 0, so
a(3.1)^2 +5 = 0
a = 5/(3.1)^2 = 0.521
y = 0.521 x^2 + 5
Respond to this Question
Similar Questions

Physics
A ball is tossed straight up into the air with an initial velocity of +15 m/s and at a height (from where it leaves the thrower's hand) of 2.0 m off the ground. Once the ball leaves the thrower's hand, it accelerates at 9.8m/s/s. … 
physics
Julie throws a ball to her friend Sarah. The ball leaves Julie's hand a distance 1.5 meters above the ground with an initial speed of 12 m/s at an angle 35 degrees; with respect to the horizontal. Sarah catches the ball 1.5 meters … 
kvb
Sam hits a golf ball with a fiveiron a distance of 120 m horizontally. A tree 45 m high and 35 m in front of Sam is directly in the path of the ball. Will the ball clear the tree if the ball makes a parabolic curve and has maximum … 
physics
A 2.25 kg ball experiences a net force of 965 N up a ramp. Once the ball reaches the top of the ramp, the force no longer acts. The force acts over a distance of 1.50 m on the ramp. Find the horizontal distance x that the ball travels … 
Physics
A small ball rolls horizontally off the edge of a tabletop of height h. It strikes the floor a distance x horizontally away from the edge of the table. (Use any variable or symbol stated above along with the following as necessary: … 
Physics
A ball is rolled off a table that is 0.481 m above the floor. The ball is rolling with a velocity if 1.8 m/s as it goes off the edge of the table. At the exact instant the first ball rolls off the table a second ball is dropped from … 
Physics
A 0.60kg basketball is dunked vertically downward so that it leaves the [layer's hand at 8m/s. Assume it is released when the bottom of the ball is at the rim (3.05 meters off the ground). a). find acceleration of the ball once it … 
Physics
A 0.60kg basketball is dunked vertically downward so that it leaves the [layer's hand at 8m/s. Assume it is released when the bottom of the ball is at the rim (3.05 meters off the ground). a). find acceleration of the ball once it … 
physics
Ball A with a mass of 0.500 kg is moving east at a velocity of 0.800 m/s. It strikes ball B, also of mass 0.500 kg, which is stationary. Ball A glances off B at an angle of 40.0° north of its original path. Ball B is pushed along … 
Physics trajectory
A ball rolls off a deck at a speed of 0.7 m/s. The deck is 4.5m above the street. How long does it take for the ball to reach the street?