If you are asking what the volume of the cube is it would be 20.3 - 17.5 ml so 2.8 ml.
(a) 3.56 m/s
(b) 11 - 3.72a
(c) t = 5.9 s
(d) -11 m/s
For most of these problems, you're being asked the velocity of the rock as a function of t, while you've been given the position as a function of t. So first calculate the first derivative of the position function using the power rule.
y = 11t - 1.86t^2
y' = 11 - 3.72t
Now that you have the first derivative, it will give you the velocity as a function of t.
(a) Velocity after 2 seconds.
y' = 11 - 3.72t
y' = 11 - 3.72*2 = 11 - 7.44 = 3.56
So the velocity is 3.56 m/s
(b) Velocity after a seconds.
y' = 11 - 3.72t
y' = 11 - 3.72a
So the answer is 11 - 3.72a
(c) Use the quadratic formula to find the zeros for the position function y = 11t-1.86t^2. Roots are t = 0 and t = 5.913978495. The t = 0 is for the moment the rock was thrown, so the answer is t = 5.9 seconds.
(d) Plug in the value of t calculated for (c) into the velocity function, so:
y' = 11 - 3.72a
y' = 11 - 3.72*5.913978495
y' = 11 - 22
y' = -11
So the velocity is -11 m/s which makes sense since the total energy of the rock will remain constant, so it's coming down at the same speed as it was going up.
Answer:
The change in the centripetal acceleration of the brother,
Δa = V₂²/R - V₁²/R
Explanation:
Given data,
A sister spins her brother in a circle of radius, R
The angular velocity of the brother, ω₁ = V₁/R
The angular velocity of the brother, ω₂ = V₂/R
The centripetal acceleration is given by the relation
a = V²/R
Therefore change in the centripetal acceleration of the brother,
Δa = V₂²/R - V₁²/R
Answer:
0.22m/s
Explanation:
The total momentum of the System is conserved. Total momentum of the system before the collision is equal to the total momentum of the system after collision. The total momentum is the sum of individual momentum of all the objects in that system.
momentum of an object = mass* velocity
Total Momentum before collision = 0.2*0.3 + 0.1*0.1= 0.07 kg⋅m/s;
Total momentum after collision = 0.1*0.26 + 0.2*x = 0.07;
Solve for x.
Answer:
817.5 Pa
Explanation:
From Bernoulli's equation, considering thst there is no height difference then
P1+½d(v1)²=P2+½d(v2)²
P1-P2=½d(v2²-v1²)
∆P=½d(v2²-v1²)
Where P represent pressure, d is density and v is velocity. Subscripts 1 and 2 represent inside and outside. ∆P is tge change in pressure
Given the speed at roof top as 128 km/h, we convert it to m/s as follows
128*1000/3600=35.555555555555=35.56 m/s
Velocity at the bottom of roof is 0 m/s
Density is given as 1.293 kg/m³
∆P=½*1.293*(35.56²-0)=817.5 Pa
