Free fall, hit the target, projectile problem

In summary, using kinematic motion equations, it can be determined that the suspect who hit the monkey is suspect A, who was on a building 65.2 meters tall, 81 meters away from the monkey, with a velocity of 55 m/s at an angle of 10 degrees. This was calculated by finding the time when the dart and monkey were at the same vertical height and checking for the same horizontal displacement at that time.
  • #1
annakwon
3
0

Homework Statement



monkey is a building 79.3 meters tall. as he was free falling, he was shot by a suspect with a dart. which suspect hit the monkey?

Suspect a - on a building 65.2 tall, 81meters away from monkey (building to building horizontally), at velocity 55, at angle 10

suspect b - 21.5/40/56.2/59
suspect c - 6.5/59.3/45.2/47

Homework Equations


kinematic motion


The Attempt at a Solution



Monkey's vertical height from ground = y1 = 79.3 - 1/2gt² = 79.3 - 4.905t²
Dart's vertical height from ground = y2 = 65.2 + Voy(t) - 1/2gt²
Voy = 55(sin 10°) = 9.55 m/s
y2 = 65.2 + 9.55t - 4.905t²
The only time instant monkey can be hit by dart is when:
y1 = y2
79.3 - 4.905t² = 65.2 + 9.55t - 4.905t²
79.3 = 65.2 + 9.55t
9.55t = 14.1
t = 14.1/9.55 = 1.4764 s <= critical time instant
horizontal displacement of dart at t = R
R = Vox(t)
Vox = 55(cos 10°) = 54.2 m/s
R = (54.2)(1.4764) ≈ 80.0 m <=> 81.0 m {dart misses monkey by 1 m}

i can do the other two, but i just need to make sure if my logically thought process is in the right direction.
 
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  • #2
Ignore the setup for a moment.
Neglecting air friction - which falls faster, the dart or the monkey?
Ergo - where do you have to be aiming to hit the monkey?
Which suspect is doing that?

Of course, I have not sketched the situations so it may not be the problem I'm thinking of.
Anyway - your reasoning looks OK. You are finding the time that the dart from each suspect has the same height as the monkey and then check that the x-positions also coincide at that time.
 

1. What is free fall?

Free fall is the motion of an object falling under the sole influence of gravity. It is a type of linear motion where the object experiences a constant acceleration towards the ground.

2. How do you calculate the time of free fall?

The time of free fall can be calculated using the equation t = √(2h/g), where t is the time in seconds, h is the initial height of the object in meters, and g is the acceleration due to gravity (9.8 m/s²).

3. What is the formula for calculating the distance traveled during free fall?

The formula for calculating the distance traveled during free fall is d = 1/2gt², where d is the distance in meters, g is the acceleration due to gravity (9.8 m/s²), and t is the time in seconds.

4. How do you solve a projectile problem?

To solve a projectile problem, you must first identify the initial velocity, angle of launch, and height of the object. Then, you can use the equations of motion to calculate the time, distance, and velocity of the object at any given point in its trajectory.

5. What factors affect the trajectory of a projectile?

The trajectory of a projectile is affected by the initial velocity, angle of launch, air resistance, and the force of gravity. Other factors such as wind, air density, and the shape of the object can also have an impact on the trajectory.

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