Answer:
option (B) is the correct option.
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Answer:
Solution:
we have given the equation of motion is x(t)=8sint [where t in seconds and x in centimeter]
Position, velocity and acceleration are all based on the equation of motion.
The equation represents the position. The first derivative gives the velocity and the 2nd derivative gives the acceleration.
x(t)=8sint
x'(t)=8cost
x"(t)=-8sint
now at time t=2pi/3,
position, x(t)=8sin(2pi/3)=4*squart(3)cm.
velocity, x'(t)=8cos(2pi/3)==4cm/s
acceleration, x"(t)==8sin(2pi/3)=-4cm/s^2
so at present the direction is in y-axis.
Answer:
The helicopter was 1103.63 meters high when the package was dropped.
Explanation:
We consider positive speed as a downward movement
y: height (m)
t: time (s)
v₀: initial speed (m/s)
Δy = v₀t + 
gt²
Δy= 15
×15 s + ×9.81
×(15 s)²
Δy= 1103.63 m
To prevent the crate from slipping, the maximum force that the belt can exert on the crate must be equal to the static friction force.
Ff = 0.5 * 16 * 9.8 = 78.4 N
a = 4.9 m/s^2
If acceleration of the belt exceeds the value determined in the previous question, what is the acceleration of the crate?
In this situation, the kinetic friction force is causing the crate to decelerate. So the net force on the crate is 78.4 N minus the kinetic friction force.
Ff = 0.28 * 16 * 9.8 = 43.904 N
Net force = 78.4 – 43.904 = 34.496 N
To determine the acceleration, divide by the mass of the crate.
a = 34.496 ÷ 16 = 2.156 m/s^2
Answer:
Explanation:
Let pressure at surface of earth be P Pa.
pressure at height of 8.1 km in air can be calculated as follows .
pressure due to column of air of 8.1 km height
= h d g , h is height , d is density of air and g is acceleration due to gravity
= 8.1 x 1000 x .87 x 9.8 = 6.9 x 10⁴ Pa .
pressure at the height of 8.1 km
= P - 6.9 x 10⁴ Pa
Pressure due to column of 16 m in the sea
= h d g
16 x 1000 x 9.8
= 15.68 x 10⁴ Pa .
Pressure at depth of 16m
= P + 15.68 x 10⁴
pressure difference between points at height of 8.1 km and pressure at point 16 m deep
= P + 15.68 x 10⁴ - P + 6.9 x 10⁴ Pa
= 22.58 x 10⁴ Pa .
