Answer:
35 kg
Explanation:
From the question,
Momentum (I) = mass (m) × velocity (v)
I = m×v................... Equation 1
Where m = mass, v = velocity
make m the subject of the equation
m = I/v.................... Equation 2
Given: I = 140 kgm/s, v = 4 m/s
Substitute these values into equation 2
m = 140/4
m = 35 kg
Hence the mass of the dart is 35 kg
According to Hooke's law, Force = spring constant x displacement of the spring. Spring constant = Force/displacement in spring = 45/0.14 = 321.42 N/m. Hope this helps!
Answer:
H = 1/2 g t^2 where t is time to fall a height H
H = 1/8 g T^2 where T is total time in air (2 t = T)
R = V T cos θ horizontal range
3/4 g T^2 = V T cos θ 6 H = R given in problem
cos θ = 3 g T / (4 V) (I)
Now t = V sin θ / g time for projectile to fall from max height
T = 2 V sin θ / g
T / V = 2 sin θ / g
cos θ = 3 g / 4 (T / V) from (I)
cos θ = 3 g / 4 * 2 sin V / g = 6 / 4 sin θ
tan θ = 2/3
θ = 33.7 deg
As a check- let V = 100 m/s
Vx = 100 cos 33.7 = 83,2
Vy = 100 sin 33,7 = 55.5
T = 2 * 55.5 / 9.8 = 11.3 sec
H = 1/2 * 9.8 * (11.3 / 2)^2 = 156
R = 83.2 * 11.3 = 932
R / H = 932 / 156 = 5.97 6 within rounding
<h2>Answer:</h2>
<u>Acceleration is </u><u>-10.57 rad/s² </u>
<u>Time is </u><u>6 seconds</u>
<h2>Explanation:</h2><h3>a) </h3>
u=900rpm= 94.248 rad/s
v =300rpm= 31.416 rad/s
s=60 revolutions= 377 rad
v²= u²+ 2as
31.416² = 94.248²+ 2 * a * 377
a = v²-u² / 2s
a= -10.57 rad/s²
<h3>b) </h3>
Using 1st equation of motion
v-u/a = t
Putting the values
t = (31.4 - 94.2)/-10.57
t = 6 seconds
