Hello everyone, I need help with this question:

A dart gun is fired while being held horizontally at a height of 1.00m above ground level and while it is at rest relative to the ground. The dart from the gun travels a horizontal distance of 5.00m. A college student holds the same gun in a horizontal position while sliding down a 45.0 degree incline at a constant speed of 2.00m/s. How far will the dart travel if the student fires the gun while it is 1.00m above the ground?

Thanks very much!

Elena's answer is wrong

last step should be 12.48(0.33)
answer is 4.12m

the time is supposed to be given , it was 0.329

To find the horizontal distance the dart will travel when the student fires the gun, we first need to analyze the motion of the dart in both situations:

1. When the dart gun is fired at rest:
- The dart is fired horizontally, meaning it has an initial horizontal velocity of 0 m/s and only experiences horizontal motion.
- The only force acting on the dart is the force of gravity, pulling it downward. This force does not affect the horizontal motion of the dart.
- The dart falls freely under the influence of gravity, following a parabolic trajectory.
- The horizontal distance traveled by the dart can be determined using the time it takes the dart to fall from 1.00 m to the ground, which we can find using the formula for free fall: t = sqrt((2h)/g), where h is the initial height and g is the acceleration due to gravity.

2. When the student fires the gun while sliding down the incline:
- The student's constant speed of 2.00 m/s does not affect the horizontal motion of the dart since it is fired horizontally.
- The dart experiences the force of gravity pulling it downward as well as a horizontal force due to the initial velocity imparted by the gun.
- The horizontal velocity of the dart is affected by the initial velocity imparted by the gun and any horizontal component of the velocity of the student sliding down the incline.

Now, let's find the solutions step by step:

1. When the dart gun is fired at rest:
- The initial height of the dart above the ground, h = 1.00 m.
- The acceleration due to gravity, g ≈ 9.8 m/s^2.
- Using the formula t = sqrt((2h)/g), we can calculate the time it takes for the dart to fall from 1.00 m to the ground.
- Plug in the values into the formula: t = sqrt((2 * 1.00) / 9.8).
- Calculate the time t.

2. When the student fires the gun while sliding down the incline:
- The student's constant speed, v = 2.00 m/s.
- The horizontal velocity of the dart is equal to the horizontal component of the student's velocity, which is 2.00 m/s.
- The dart experiences the same acceleration due to gravity, g ≈ 9.8 m/s^2.
- The time taken for the dart to travel a certain horizontal distance is the same as the time taken for the student to slide down the incline by the same distance.
- Use the formula d = v * t to find the horizontal distance traveled by the dart.
- Plug in the values into the formula: d = (2.00 m/s) * t.
- Calculate the horizontal distance d using the calculated value of t from step 1.

Hope this helps! Let me know if you need further clarification on any step.

(a)

h=gt²/2 =>
t =sqrt(2h/g)=
=sqrt(2•1/9.8) =0.45 s
s=v(x) •t =>
The dart initial speed is
v(x) = s/t =5/0.45=11.07 m/s.
(b) v(y) =v•sin45º=2•0.707 =1.41m/s
h=v(y) •t +gt²/2
gt²/2 + v(y) •t –h =0,
4.9 t² +1.41•t -1 =0
t1=0.33 s. t2 - negative root
s1=v(x) •t1= 11.07•0.33=3.66 m.

As far as it wants! Your most welcome! :-)