Projectile Motion, A study of height and time

AI Thread Summary
The discussion centers on a physics problem involving projectile motion, specifically a rocket launched at 97.0 m/s at a 53.0° angle, aimed at a 27.0 m high wall located 24.0 m away. The calculations provided show that the rocket reaches a height of 31 m at the wall, suggesting it clears the wall by 4.00 m. However, there is uncertainty about the accuracy of these calculations, with participants questioning whether an error exists. The conversation highlights the importance of verifying calculations in physics problems and suggests that the solution may need reevaluation. Ultimately, the accuracy of the initial calculations is in question, prompting a call for further analysis.
mmiller39
Messages
32
Reaction score
0
A Cutnell and Johnson Physics question illustrates a rocket launch:

A rocket is fired at a speed of 97.0 m/s from ground level, at an angle of 53.0 ° above the horizontal. The rocket is fired toward an 27.0-m high wall, which is located 24.0 m away. The rocket attains its launch speed in a negligibly short period of time, after which its engines shut down and the rocket coasts. By how much does the rocket clear the top of the wall?

My Calculations:

Vo = 97.0 m/s
Theta = 53 degrees
x = 24 m
y = 27 m
Let H illustrate the height of the rocket at point x on the axis.
t = ?
a = -9.80 m/s ^2

Vo sin 53 = Voy = 77.46
Vo cos 53 = Vox = 58.37

x = Vox(t)
t = x/Vox = 24/58.37 = .411 s

H = Voy(t) + .5 a(t^2)

Plug and Chug

H = 77.46(.411) + .5(-9.80)(.411^2) = 31 m

Distance Rocket clears wall = 31m-27m = 4.00 m <-----Incorrect.

Is there a problem with my calculations that I am not understanding?
 
Physics news on Phys.org
How do u no ur wrong? Looks ok 2 me unless I am makin exactly the same mistake. Mayb ur lookin under the wrong chapter at the back of the book 4 ur answers!?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Projectile Motion - vertical displacement at specific time.
Replies
3
Views
2K
What is the total distance traveled by a bullet fragment after an explosion?
Replies
13
Views
2K
Find the height of a lamp based on the velocities of projectiles
Replies
40
Views
2K
Attempt to jump across a river on a motorcycle
Replies
2
Views
3K
How Do You Solve a Projectile Motion Problem?
Replies
3
Views
4K
How Do You Calculate Maximum Height and Range of a Projectile?
Replies
1
Views
1K
Needing some help about time of flight of a launched ball/horiz range
Replies
6
Views
3K
Projectile Motion Experimental Error
Replies
1
Views
2K
Projectile Motion - object that is shot at an angle of 55 degrees
Replies
8
Views
2K
Projectile motion question-nothing special.
Replies
6
Views
6K

Hot Threads

Recent Insights

Back
Top