Projectiles thrown at an angle

In summary, the first problem involves calculating the initial speed of a golf ball and its maximum height reached when it lands 210 m downrange on a level course, neglecting air friction. The second problem involves finding the height reached by a ball thrown from a train traveling at a constant speed, with an initial angle of 65.0° with the horizontal. The third problem involves calculating the position and time of a car that rolls down an incline and falls off a cliff into the ocean due to defective brakes. These problems can be solved using the range and height equations for projectile motion.
  • #1
shellz178
3
0
i'm having a lot of trouble with these:

1. A golf ball with an initial angle of 36° lands exactly 210 m down the range on a level course.
(a) Neglecting air friction, what initial speed would achieve this result?

(b) Using the speed determined in item (a), find the maximum height reached by the ball.

2. A science student riding on a flatcar of a train moving at a constant speed of 5.00 m/s throws a ball toward the caboose along a path that the student judges as making an initial angle of 65.0° with the horizontal. The teacher, who is standing on the ground nearby, observes the ball rising vertically. How high does the ball rise?

if anyone knows how to do these, help would be amazing. thanks!
 
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  • #2
shellz178 said:
i'm having a lot of trouble with these:

1. A golf ball with an initial angle of 36° lands exactly 210 m down the range on a level course.
(a) Neglecting air friction, what initial speed would achieve this result?

(b) Using the speed determined in item (a), find the maximum height reached by the ball.

Here, this should be useful: http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Vectors/ProjectilesMotion.html" [Broken].

After showing us some of your work, we'll be glad to jump in if necessary.
 
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  • #3
shellz178 said:
i'm having a lot of trouble with these:

1. A golf ball with an initial angle of 36° lands exactly 210 m down the range on a level course.
(a) Neglecting air friction, what initial speed would achieve this result?

(b) Using the speed determined in item (a), find the maximum height reached by the ball.

2. A science student riding on a flatcar of a train moving at a constant speed of 5.00 m/s throws a ball toward the caboose along a path that the student judges as making an initial angle of 65.0° with the horizontal. The teacher, who is standing on the ground nearby, observes the ball rising vertically. How high does the ball rise?

if anyone knows how to do these, help would be amazing. thanks!


(a) Use the range equation: [tex]X_f[/tex] - [tex]X_i[/tex] = [tex]\frac{V_i^2sin(2\theta)}{g}[/tex]
 
Last edited:
  • #4
The range of a projectile (how far it travels) is given by the equation
v2sin2@/g

note: i unconventionally used @ for the angle

The height is given by
h=v2sin2@/2g

These equations are derived from the basic kinematic equations of projectile motion under constant acceleration, have fun!
 
  • #5
thanks a lot for all the help, i got the first question. I'm still stuck on the second one, and what's worse is that i have another one:

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 6.50 m/s2 and travels 50.0 m to the edge of the cliff. The cliff is 40.0 m above the ocean.
(a) What is the car's position relative to the base of the cliff when the car lands in the ocean?

(b) How long is the car in the air?

i don't know if something's wrong with me because i can calculate upward angles, but downward angles won't work the same way.
 
  • #6
thanks a lot for all the help, i got the first question. I'm still stuck on the second one, and what's worse is that i have another one:

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 6.50 m/s2 and travels 50.0 m to the edge of the cliff. The cliff is 40.0 m above the ocean.
(a) What is the car's position relative to the base of the cliff when the car lands in the ocean?

(b) How long is the car in the air?

i don't know if something's wrong with me because i can calculate upward angles, but downward angles won't work the same way.
 

What is a projectile thrown at an angle?

A projectile thrown at an angle is an object that is thrown or launched into the air at an angle, rather than directly upwards or horizontally.

What factors affect the trajectory of a projectile thrown at an angle?

The factors that affect the trajectory of a projectile thrown at an angle include the initial velocity, the angle of launch, the force of gravity, and air resistance.

How does the initial velocity affect the trajectory of a projectile?

The initial velocity, or the speed at which the projectile is launched, affects the distance and height that the projectile will travel. A higher initial velocity will result in a longer horizontal distance and a higher peak height.

What is the optimal angle for maximum distance in a projectile thrown at an angle?

The optimal angle for maximum distance in a projectile thrown at an angle is 45 degrees. This angle allows for the perfect balance between horizontal and vertical velocities, resulting in the longest possible distance.

How does air resistance affect the trajectory of a projectile thrown at an angle?

Air resistance, or drag, acts in the opposite direction of the projectile's motion and can decrease its velocity and distance traveled. The effect of air resistance is greater at higher speeds and angles, so it can significantly alter the trajectory of a projectile thrown at an angle.

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