Engineering Mechanics - Kinematics of Particle (KOP) - Discussion

Discussion :: Kinematics of Particle (KOP) - General Questions (Q.No.32)

32. 

For a short time the missile moves along the parabolic path y = (18 - 2x2) km. If motion along the ground is measured as x = (4t - 3) km, where t is in seconds, determine the magnitudes of the missile's velocity and acceleration when t = 1 s.

[A]. v = 5.66 km/s, a = 4.0 km/s2
[B]. v = 16.49 km/s, a = 64.0 km/s2
[C]. v = 16.00 km/s, a = 22.6 km/s2
[D]. v = 4.00 km/s, a = 16.03 km/s2

Answer: Option B

Explanation:

No answer description available for this question.

Hermes said: (Aug 16, 2021)  
y = 18 - 2x^2,
= 18 -2(4t-3)^2,
= -32t^2 + 48t.

Vy = dy/dt,
= -64t + 48.

ay = dv/dt,
= -64.

x = 4t -3.
Vx = dx/dt.
= 4,

ax = dx/dt.
= 0.

when t = 1s.
Vy = -16 km/s^2,
Vx = 4 km/s^2.
v = √(Vy^2 + Vx^2),
= 16.49 km/s^2.

ay = -64 km/s^2.
ax = 0 km/s^2,
a = √(ax^2 + ay^2),
= 64 km/s^2.

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