A toy rocket is launched from a
4.2
$m$ high platform in such a way that its height, $h$ (in meters), after $t$ seconds is given by the equation $h = - 4.9 t^{2} + 28.7 t + 4.2$
How long will it take for the rocket to hit the ground?

Answer

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Answer

$6$ seconds is the time it will take for the rocket to hit the ground.

Steps

Step 1 ：Given the equation for the height of the rocket as $h = - 4.9 t^{2} + 28.7 t + 4.2$ , we need to find the time $t$ when the rocket hits the ground, i.e., when $h = 0$ .

Step 2 ：This is a quadratic equation in the form $a t^{2} + b t + c = 0$ , where $a = - 4.9$ , $b = 28.7$ , and $c = 4.2$ .

Step 3 ：We can solve this equation using the quadratic formula $t = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .

Step 4 ：Substituting the values of $a$ , $b$ , and $c$ into the formula, we get two solutions for $t$ .

Step 5 ：However, since time cannot be negative, we discard the negative solution and keep the positive one.

Step 6 ： $6$ seconds is the time it will take for the rocket to hit the ground.

A toy rocket is launched from a4.2m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h=−4.9t2+28.7t+4.2How long will it take for the rocket to hit the ground?

Answer

Popular Problems

A toy rocket is launched from a
4.2
$m$ high platform in such a way that its height, $h$ (in meters), after $t$ seconds is given by the equation $h = - 4.9 t^{2} + 28.7 t + 4.2$
How long will it take for the rocket to hit the ground?