(4 pts) If a rock is thrown vertically upward from the surface of Mars with an initial velocity of 15m/sec
1 answer:
Answer:
Step-by-step explanation:
I see you're in college math, so we'll solve this with calculus, since it's the easiest way anyway.
The position equation is
That equation will give us the height of the rock at ANY TIME during its travels. I could find the height at 2 seconds by plugging in a 2 for t; I could find the height at 12 seconds by plugging in a 12 for t, etc.
The first derivative of position is velocity:
v(t) = -3.72t + 15 and you stated that the rock will be at its max height when the velocity is 0, so we plug in a 0 for v(t):
0 = -3.72t + 15 and solve for t:\
-15 = -3.72t so
t = 4.03 seconds. This is how long it takes to get to its max height. Knowing that, we can plug 4.03 seconds into the position equation to find the height at 4.03 seconds:
s(4.03) = -1.86(4.03)² + 15(4.03) so
s(4.03) = 30.2 meters.
Calculus is amazing. Much easier than most methods to solve problems like this.
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Answer:
The maximum height of the marshmallow is 49 feet.
Step-by-step explanation:
The vertex form of a parabola is
.... (1)
Where, (h,k) is vertex of the parabola is a is constant.
The given function is
..... (2)
Where, h is height of the marshmallow (in feet) and t is the time (in seconds) after he throws the marshmallow.
From equation (1) and (2), we get
The value of a is -16, which is less than 0. So, the given function is a downward parabola.
The vertex of a downward parabola is the point of maxima.
The value of h is 14 and the value of k is 49. So, the vertex of the parabola is (14,49). It means the maximum height of the marshmallow is 49 feet in 14 seconds.
Therefore the maximum height of the marshmallow is 49 feet.
Answer:
I have attached a photo. that might help you out.
