Projectile Motion Given only angle and distance?

In summary, to calculate the minimum speed needed to clear the canyon, we can use the equations d = v_x t and h = v_y t - 1/2gt^2, where d is the distance between the canyon walls, v_x and v_y are the horizontal and vertical velocities respectively, and g is the acceleration due to gravity. These equations can be solved for the time to cross the canyon and the height reached at the other side, which will allow us to calculate the minimum speed required using the formula v^2_f = v^2_i + 2ad.
  • #1
APSurvivor
1
0

Homework Statement



A person decides to jump a canyon. The walls are equally high and 10 meters apart. He takes off by driving a motorcycle up a short ramp sloped at 11 degrees. What minimum speed must he have to clear the canyon?

Homework Equations



I don't know if these are correct or not

(Time in Air)
h= Vyt + 1/2gt[itex]^{2}[/itex]

(distance)
d= Vxt

Vx= Vcos11
Vy= Vsin11

Other Formulas
V[itex]^{2}[/itex]f= V[itex]^{2}[/itex]i + 2ad


The Attempt at a Solution



my sad attempt lol

Vi=?
Vf=?
h=?
d= 10 meters
angel= 11 degrees
g(or a)= 9.8m/s[itex]^{2}[/itex]


(Time in Air)
h= Vyt + 1/2gt[itex]^{2}[/itex]
h= Vsin11t -4.9t[itex]^{2}[/itex]


(Distance)
d= Vxt
10= Vcos11t


Am I thinking this through right? Or am I way off??
 
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  • #2
Hi APSurvivor, welcome to Physics Forums.

You're close to the right track, but not quite there yet.

You've got expressions for the vertical and horizontal velocities in terms of the (unknown) initial speed, v. That's good.

When you write the two expressions for the trajectory components, vertical and horizontal, in terms of these velocities and times you got your two expressions:

[itex] d = v_x t [/itex]
[itex] h = v_y t - \frac{1}{2} g t^2 [/itex]

Now, which expression would be simplest to solve for the time to cross the canyon?

When the person reaches the other side of the canyon, what will be his height h with respect to the launch point?
 

FAQ: Projectile Motion Given only angle and distance?

1. How do you calculate the initial velocity for a projectile given only the angle and distance?

To calculate the initial velocity, we use the formula v = d/t, where v is the initial velocity, d is the distance, and t is the time. Since we are given the angle and distance, we can use trigonometric functions to determine the horizontal and vertical components of the initial velocity, and then use the Pythagorean theorem to find the magnitude of the initial velocity.

2. What is the formula for the maximum height reached by a projectile given only the angle and distance?

The formula for the maximum height reached by a projectile is h = (v^2 * sin^2(theta)) / (2 * g), where h is the maximum height, v is the initial velocity, theta is the angle, and g is the acceleration due to gravity. Using this formula, we can find the maximum height reached by the projectile at any given angle and distance.

3. How does the angle affect the range of a projectile?

The range of a projectile is directly affected by the angle at which it is launched. The greater the angle, the greater the range. This is because a higher angle results in a higher initial velocity in the horizontal direction, allowing the projectile to travel farther before hitting the ground.

4. Can you determine the time of flight for a projectile given only the angle and distance?

Yes, the time of flight can be calculated using the formula t = d / (v * cos(theta)), where t is the time of flight, d is the distance, v is the initial velocity, and theta is the angle. This formula is derived from the horizontal component of the projectile's motion.

5. How does air resistance affect the motion of a projectile given only the angle and distance?

Air resistance can affect the motion of a projectile by reducing its velocity and altering its trajectory. However, if the projectile is launched at a low velocity and the distance is relatively short, the effects of air resistance may be negligible. In this case, the projectile's motion can be calculated using the same formulas as for a projectile without air resistance.

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