A missile launched at a velocity of 30.0 m/s at an angle of 30.0 to the normal. What is the maximum height the missile attains?
sin 60 = 0.866025404
0.866025404 x 30 = 25.98076211
25.98076211 x 25.98076211 / 2 / 9.8 = 34.4 m
Did you see the reply on 1 April at 11:44pm about this problem?
yes but I don't understand I just change the sin 30 to sin 60 like you said
h = V^2sin^2(µ)/2g
h = 30^2sin^2(60º)/2(9.8)= 34.4m.
I am first pasting the previous response. Then, I will step through the steps.
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Break the problem into vertical and horizontal components. Find the initial vertical component (30.0 m/s) * sin(60) because the problem says the missile is launched 30 degress from the NORMAL.
Determine how long before the vertical velocity is 0. That will be the maximum height. Plug that time into the distance equation:
t = time
g=gravity acceleration
distance = (initial velocity) * t + (1/2)(g)(t^2)
Remember that for positive up, gravity will be a negative acceleration.
So, pay attention to the sign of the second term.
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Here is a non-calculus way to solve this.
First, when the missle is launched it goes up until gravity eventually slows it to a zero vertical speed. That is the maximum height.
Find the initial vertical velocity.
(initial vertical velocity) = (initial velocity) * sin(60)
or
25.98 m/s = (30.0m/s)*(0.8660
Now to find how long before the vertical velocity is 0 (of course immediately after that the velocity will be increasing in the DOWN direction).
The formula for veocity (only using vertical) is:
velocity = (initial velocity) + (acceleration)*(time)
use t for time
We want to know when the velocity is 0.
0.0 = (25.98 m/s) - (gravity)* t
The second term is subtracted because the acceleration (gravity) is in the negative direction.
0.0 = (25.98 m/s) - (9.8 m/s^2)*t
arranging...
(9.8 m/s^2)*t = 25.98 m/s
finally...
t = 2.651 seconds
This is the time where the missile will be the highest.
How high is that?
A handy distance formula is:
Here distance is vertical or height.
height = (initial distance) + (initial velocity) * t) + (0.5)*(g)*(t^2)
Note the minus sign in the term with gravity.
height = 0.0m + (25.98 m/s) * t - (0.5)*(9.8 m/s^2)* t^2
height = (25.98 m/s) * (2.651 s) - (4.9 m/s^2)*(7.028 s^2)
height = 68.87m - 34.43m
height = 34.44m
34.4m
Why did the missile go to therapy? Because it had some serious height issues! But don't worry, it reached a maximum height of approximately 34.4 meters. Keep reaching for the stars, rocket!
To find the maximum height attained by the missile, we can use the kinematic equations of motion.
First, we need to resolve the initial velocity of the missile into its horizontal and vertical components. The initial velocity of 30.0 m/s is at an angle of 30.0 degrees to the normal.
The horizontal component of the velocity can be found by multiplying the initial velocity by the cosine of the angle.
Horizontal component = 30.0 m/s * cos(30.0 degrees) = 30.0 m/s * 0.866025404 = 25.98076211 m/s
The vertical component of the velocity can be found by multiplying the initial velocity by the sine of the angle.
Vertical component = 30.0 m/s * sin(30.0 degrees) = 30.0 m/s * 0.5 = 15.0 m/s
Now, we can use the kinematic equation for vertical motion to find the maximum height.
The equation we can use is:
Vertical displacement = (vertical component of velocity)^2 / (2 * acceleration due to gravity)
In this equation, the acceleration due to gravity is approximately 9.8 m/s^2.
So, plugging in the values:
Vertical displacement = (15.0 m/s)^2 / (2 * 9.8 m/s^2) = 225 m^2/s^2 / (19.6 m/s^2) = 11.48 m^2
Therefore, the maximum height attained by the missile is approximately 11.48 meters.