Question

1. a model airplane takes off at a constant rate of 17 feet per second. its height, in feet, after t seconds is given by h = 17t. at the same time, a ball is launched from ground level with an initial velocity of 35 feet per second. the height of the ball, in feet, after t seconds is given by the equation h = -16t² + 35t. find the time it takes for the collision to occur. round your answer to the thousandths place.

Explanation:

Step1: Igualar las ecuaciones de altura

$$17t=-16t^{2}+35t$$

Step2: Reordenar la ecuación

$$16t^{2}+17t - 35t=0$$
$$16t^{2}-18t = 0$$

Step3: Factorizar la ecuación

$$t(16t - 18)=0$$

Step4: Resolver para \(t\)

Si \(t = 0\), es el tiempo inicial.
Para \(16t-18=0\), entonces \(16t=18\), \(t=\frac{18}{16}=\frac{9}{8}=1.125\)

Answer:

\(t = 1.125\)