The time that the rocket will hit the ground is after 2.78 seconds.
Step-by-step explanation:
You know that the height (H) is given by the formula H= -16*t² + v*t+ h
A rocket is launched directly from the side of a 40 m high cliff and that the initial velocity is 30 m / sec. So this indicates that the value of v is 30 m / sec and h is the height of 40 m. Replacing this value in the formula you get:
H= -16*1²+ 30*t+ 40
You must find the moment when the rocket will hit the ground, that is, the moment when the height H is zero:
0-16*12+ 30*t+ 40
To calculate the time t the expression is used: -b+ √b²-4*a*c - 2*a
Being the general quadratic equation ax² + bx + c = 0, in this case a=-16, b=30 and c= 40. Replacing:
Solving;
-30+ 302-4*(-16)*40 2*(-16)
Solving:
-30+ √900+2,560 2*(-16)
-30+-√3,460 2*(-16)
-30+-58.82 2*(-16)
Then: t1 = 30+58.82 2*(-16)
Solving for t1: or t2 = -30-58.82 2*(-16)
t1 = 28.82 2*(-16)
t1 = 28.82 -32
t1=-0.9
Solving for t2: t2
= -88.82 2*(-16)
t2 = -88.82 -32
t2=2.78
Since the time cannot be negative, the time that the rocket will hit the ground is after 2.78 seconds.
Answers & Comments
Answer:
The time that the rocket will hit the ground is after 2.78 seconds.
Step-by-step explanation:
You know that the height (H) is given by the formula H= -16*t² + v*t+ h
A rocket is launched directly from the side of a 40 m high cliff and that the initial velocity is 30 m / sec. So this indicates that the value of v is 30 m / sec and h is the height of 40 m. Replacing this value in the formula you get:
H= -16*1²+ 30*t+ 40
You must find the moment when the rocket will hit the ground, that is, the moment when the height H is zero:
0-16*12+ 30*t+ 40
To calculate the time t the expression is used: -b+ √b²-4*a*c - 2*a
Being the general quadratic equation ax² + bx + c = 0, in this case a=-16, b=30 and c= 40. Replacing:
Solving;
-30+ 302-4*(-16)*40 2*(-16)
Solving:
-30+ √900+2,560 2*(-16)
-30+-√3,460 2*(-16)
-30+-58.82 2*(-16)
Then: t1 = 30+58.82 2*(-16)
Solving for t1: or t2 = -30-58.82 2*(-16)
t1 = 28.82 2*(-16)
t1 = 28.82 -32
t1=-0.9
Solving for t2: t2
= -88.82 2*(-16)
t2 = -88.82 -32
t2=2.78
Since the time cannot be negative, the time that the rocket will hit the ground is after 2.78 seconds.