Asked by Anonymous
A ship fires its guns with a speed of 400 m/s at an angle of 35 with the horizontal.
a. Find the range and maximum altitude.
b. If the ship hits a plane that was 12 km away, how high was the plane flying?
a. Find the range and maximum altitude.
b. If the ship hits a plane that was 12 km away, how high was the plane flying?
Answers
Answered by
Jai
(a) Maximum height formula for projectile motion:
H,max = (vo,y)^2 / 2g
or
H,max = (vo)^2 * sin^2 (θ) / 2g
where
vo = initial velocity
θ = angle of release (wrt to horizontal)
g = acceleration due to gravity = 9.8 m/s^2
Substituting,
H,max = (400^2) * (sin (35))^2 / (2*9.8)
H,max = ?
(b) We are given a horizontal distance of 12 km = 12000 m, and we need to find the height of the bullet after it has traveled 12000 m. Formula to use:
x = (vo,x) * t
or
x = (vo cos(θ)) * t
where
x = horizontal distance
t = time
Solving for the time,
12000 = 400 cos(35) * t
t = 12000 / 327.661
t = 36.623 s
Then we use another formula to get the height, y:
y = (vo sin(θ))t - (1/2)gt^2
Substituting,
y = (400 sin(35))(36.623) - (0.5)(9.8)(36.623)^2
y = ?
Hope this helps~ `u`
H,max = (vo,y)^2 / 2g
or
H,max = (vo)^2 * sin^2 (θ) / 2g
where
vo = initial velocity
θ = angle of release (wrt to horizontal)
g = acceleration due to gravity = 9.8 m/s^2
Substituting,
H,max = (400^2) * (sin (35))^2 / (2*9.8)
H,max = ?
(b) We are given a horizontal distance of 12 km = 12000 m, and we need to find the height of the bullet after it has traveled 12000 m. Formula to use:
x = (vo,x) * t
or
x = (vo cos(θ)) * t
where
x = horizontal distance
t = time
Solving for the time,
12000 = 400 cos(35) * t
t = 12000 / 327.661
t = 36.623 s
Then we use another formula to get the height, y:
y = (vo sin(θ))t - (1/2)gt^2
Substituting,
y = (400 sin(35))(36.623) - (0.5)(9.8)(36.623)^2
y = ?
Hope this helps~ `u`
Answered by
Anonymous
I'm sorry, but I don't think part a's equation is right, unless I read the equation wrong. The answer key says, part a is 2.7 x 103 m = 278.1 and 1.5 x 104 m = 156. Also, for part b, if I read the equation right, is the answer 14,981.3562 m?
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.