Solve Projectile Problem: Calculate Impact Speed & Angle

In summary, the car falls from a 15 meter platform and the impact angle is 9.8 degrees. The car's speed is 17.15 meters per second.
  • #1
Mo
81
0
Ack! I thought i knew this!

"A car manufacturer test crash resistance by driving test vehicles off a horiztontal platform so that they fall to a concrete surface below.If this car is driven off at 20m/s and the platform is 15m above the ground calculate the impact angle and speed"

Im not to fussed about the impact angle just yet, i tried to work the speed out...

u = 0
a = 9.8
s (displacement) = 15
v = ?
t = ?

For this i need to use the equation: [tex]v^2 = u^2 + 2as[/tex]

[tex]v^2 = 2 \times 9.8 \times 15[/tex]

[tex]v^2 =294[/tex]

[tex]v = 17.15 m/s[/tex]



But the answer in the book is different, it says 26.3 m/s

Im most probably making an incredibly stupid mistake, please spot it!

thanks,

Regards,
Mo
 
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  • #2
I'd try using the standard equations for projectile motion for constant accelertions:

[tex]x(t)=x(0) + v_x (0) t +\frac{1}{2}a_x t^2[/tex]
[tex]y(t)=y(0) + v_y (0) t +\frac{1}{2}a_y t^2[/tex]

Just find the right parameters and solve...
 
  • #3
Ahh! I've never come across those before!
 
  • #4
Well it gives you the motion (horizontal coordinate x and vertical coordinate y) as a function of time t. The first term is the initial position at t=0. The second term says the coordinates change in time proportional to the initial velocity (assuming no friction). The last term tells you how the coordinates change under a constant acceleration a.

I'm sure you understand the first two terms, and for this problem there is an acceleration (gravity!) involved so you will have to know how to use the last term or use conservation of energy.
 
  • #5
Mo said:
For this i need to use the equation: [tex]v^2 = u^2 + 2as[/tex]

[tex]v^2 = 2 \times 9.8 \times 15[/tex]

[tex]v^2 =294[/tex]

[tex]v = 17.15 m/s[/tex]
This gives you the vertical component of the velocity. Now add the horizontal component. (Don't forget that they are perpendicular.)
 
  • #6
you have already found the y component of final speed...now you need the x component
 
  • #7
Thank you very much Doc Al! . I am still a bit confused as to why we have to combine the two components , as they are completely independent of each other. But I've got the answer now and ill have to read up on it.

Thanks again

Regards,
Mo
 

1. How do I calculate the impact speed of a projectile?

To calculate the impact speed of a projectile, you will need to know the initial velocity, the angle of launch, and the distance traveled. You can use the formula v = √(u² + 2as), where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (usually 9.8 m/s²), and s is the distance traveled. This will give you the impact speed in meters per second.

2. How do I calculate the angle of impact for a projectile?

The angle of impact for a projectile can be calculated by using trigonometry. You will need to know the vertical and horizontal components of the projectile's velocity. The formula for calculating the angle is tanθ = (vy/vx), where θ is the angle, vy is the vertical velocity, and vx is the horizontal velocity.

3. What factors affect the impact speed and angle of a projectile?

The impact speed and angle of a projectile can be affected by various factors such as the initial velocity, angle of launch, air resistance, and gravitational force. The mass and shape of the projectile can also play a role in its impact speed and angle.

4. Can the impact speed of a projectile be greater than the initial velocity?

Yes, the impact speed of a projectile can be greater than the initial velocity. This can happen if the projectile is launched at an angle, as the vertical component of the velocity will add to the initial velocity, resulting in a greater impact speed.

5. How can I use projectile motion equations to solve real-world problems?

Projectile motion equations can be used to solve real-world problems, such as calculating the trajectory of a ball being thrown, the distance a rocket will travel, or the angle of a ramp needed for a car to jump a certain distance. By understanding the principles of projectile motion and using the appropriate equations, you can accurately predict the path and outcome of a projectile in various scenarios.

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