quadratic equations

Question

If one throws a ball down from a high cliff, the distance it travels can be modeled by the equation:  where t is the time in seconds and d is the distance in meters.

1. At what time will the ball hit the ground?
2. You will get two answers because this is a quadratic equation. Do both make sense? (Explain in detail Why or Why not).

Answer 1

The object wil reach the ground when the distance is distance is equals to zero.

d= -9.8t^2-15t+100

0= -9.8t^2-15t+100, you can use the quadratic formula to solve for t or graph the function and find the t-intercepts, keeping in mind that the time can not be negative ( time can not go back).

t= -b+-√b^2-4ac/(2a) a= -.98. , b=-15 and c=100

t= 15 +-√(-15)^2-4(-9.8) (100). /(2(-9.8)

t= 15 + -√96.04 +3920 / (-19.6)

t= 15 + - √4016.04/(-19.6)

t= 15 + - 63.372/ (-19.6)

t=(15 +63.372) /(-19.6) = - 3.998 ≈ -4 secs ( Do not consider this value, because t is negative.

t= (15 -63.372)/(-19.6)= 2.467 secs. , this should be your answer.

To check your finding you can graph this function in a TI-84 graphing calculator or demos calculator (free online and check the t- interceptions. you can use the following window setting to see your interceptions

x=10, x=-10, y=-10, y=125.

2) The difference between the two answers is that the time time can not be negative and the second answer is positive, which is obviously ,the answer.