Physics, 02.08.2019 17:00 samavants74

What is the maximum distance we can shoot a dart, provided our toy dart gun gives a maximum initial velocity of 5.84 m/s?

Answers: 1

Show answers

Answers

Answer from: Wolfman2004

1) The maximum distance can be reached when the dart is shot with an angle of $\theta=45^{\circ}$ above the horizontal (see demonstration of this fact at the end).

2) The motion of the dart is an uniform motion on the x-axis (horizontal direction) with constant velocity v_i = 5.84~m/s

and it is an uniformly accelerated motion on the y-axis (vertical direction), with the gravitational acceleration g=9.81~m/s^2

acting downwards. So we can write the laws of motion on both directions:
$S_x(t) =( v_i \cos{\theta}) t$
$S_y(t) = (v_i \sin{\theta})t - \frac{1}{2} gt^2$
where the negative sign means that g points downwards.

3) First of all we can find the time at which the dart reaches the ground. This can be found by requiring S_y(t)=0

:
$(v_i \sin{\theta})t - \frac{1}{2} gt^2=0$
From this we find two solutions: t=0~s

, corresponding to the beginning of the motion (so we are not interested in this one), and
$t= \frac{2 v_i \sin{\theta}}{g} =0.84~s$

4) Now that we now when the dart reaches the ground, we can use this information to find the distance covered on the x-axis, by using t=0.84~s

inside the equation of S_x(t)

written at point 2:
$S_x(0.84~s)= 5.84~m/s \cdot \cos{45^{\circ}} \cdot 0.84~s }=3.47~m$

--------------------------
DEMONSTRATION OF POINT 1:

Calling v the initial velocity of the dart, and using a coordinate system where the x-axis coincides with the horizontal direction and the y-axis with the vertical direction, we can write the law of motion on both directions:
$S_x(t) = v cos{\theta} t$
$S_y(t) = v sin{\theta} t + \frac{1}{2} g t^2$
where t is the time, $\theta$ is the initial angle of the dart, and g= -9.81 m/s^2

is the gravitational acceleration.
The maximum horizontal distance can be found by requiring that S_y=0

. This condition occurs twice: when the motion starts ( t=0

) and when the dart falls to the ground (let’s call t_s

the time at which this happens). Therefore we can find t_s

by requiring S_y(t_s)=0

, i.e.:
$v sin{\theta} t_s + \frac{1}{2} g t_s^2 =0$
which has two solutions: t_s=0

(beginning of the motion) and $t_s = - \frac{2 v sin{\theta}}{g}$ .So we can find the maximum horizontal distance covered by the dart by substituting this t_s

into the law of motion for S_x(t)

:
$S_x(t_s) = v cos\theta t_s = -\frac{2 v^2 cos\theta sin\theta}{g}$
Since
$sin2\theta = 2 cos\theta sin\theta$ ,
we can write
$S_x(t_s) = - \frac{v^2 sin2\theta}{g}$
Since g is negative, the maximum of this function occurs for $sin2\theta=1$ , and this happens when $\theta=45^{\circ}$ .

Answer from: Quest

r = ρ x length / area

ρ = r x area / length

ρ is in ohm-meters

in basic units, it is m³kg/s³a²

i think this is it.

Answer from: Quest

The answer should be a.

Another question on Physics

Physics, 22.06.2019 10:30

The uniform slender bar rests on a smooth horizon- tal surface when a force f is applied normal to the bar at point a. point a is observed to have an initial acceleration aa of 20 m/s2, and the bar has a corre- sponding angular acceleration of 18 rad /s2. deter- mine the distance b.

Answers: 1

Answer

Physics, 22.06.2019 11:20

Wave functions describe orbitals in a hydrogen atom. each function is characterized by 3 quantum numbers: n, l, and ml. if the value of n = 2: the quantum number l can have values from to . the total number of orbitals possible at the n = 2 energy level is .

Answers: 3

Answer

Physics, 22.06.2019 13:40

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

Answers: 2

Answer

Physics, 22.06.2019 16:10

Amass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. initially, the mass is released from rest from a point 8 inches below the equilibrium position. find the equation of motion. (use g = 32 ft/s2 for the acceleration due to gravity.)

Answers: 1

Answer

You know the right answer?

What is the maximum distance we can shoot a dart, provided our toy dart gun gives a maximum initial...

Questions