Welcome to your Phy set 4
1.
The magnitudes of vectors A, B, and C are 3, 4, and 5 units respectively. If A + B = C, the angle between A and B is
2.
The velocity of a particle moving in the x-y plane is dx/dt = 8πsin(2πt), dy/dt = 5πcos(2πt). At t = 0, x = 8 and y = 0. The path is
3.
A man throws balls vertically upwards at 2-second intervals with same speed. Minimum speed to have more than 2 balls in air at any time?
4.
A body revolving in a circle with uniform speed has
5.
The horizontal range of projectile is √3 times its maximum height. The angle of projection will be
6.
The scalar product of vectors is
7.
Two bodies are projected with the same velocity, one at 30° and the other at 60°. What is the ratio of their maximum heights?
8.
The direction of instantaneous velocity is shown by:
9.
A body is whirled in a horizontal circle (r = 20 cm, ω = 10 rad/s). Linear velocity is:
10.
A car moves at constant speed on a circular track (radius 100 m, lap time 62.8 s). Avg velocity and speed are:
11.
A marble dropped in a descending elevator from 2 m height takes 1.2 s to reach floor. What is elevator’s acceleration? (g = 10 m/s²)
12.
A particle moves in x-y plane: x=asin(ωt),y=acos(ωt)x = a \sin(\omega t), y = a \cos(\omega t). The path is a:
13.
In uniform circular motion, the velocity and acceleration vectors are:
14.
For projectile motion, what happens to horizontal velocity (neglecting air resistance)?
15.
A stone is tied to 1 m string and whirled in horizontal circle, 22 revolutions in 44 s. Find magnitude & direction of acceleration.
16.
Ratio of total time to time of flight for projectile from 40m tower (u=20m/s, 30°)
17.
Man swims across river flowing W→E; shortest time strategy?
18.
Trajectory: y = 2x - 9x²; find angle θ₀
19.
x = 6t, y = 8t - 5t²; angle of projection
20.
Projectile explodes at top of 16 km range; 1 part falls down, other?
21.
When x-component of vector r is max
22.
Boat speed = 5 km/h, river width = 1 km, time = 15 mins → river speed?
23.
Time period change if string length halved (circular motion)
24.
Projectile with horizontal velocity = 3 m/s² × 0.5 min, max height = 80 m
25.
Object projected on 60° and 30° inclined planes, x₁:x₂ = ?
26.
Diagonals of parallelogram are 2î, 2ĵ. Area = ?
27.
Momentum change when projectile returns to ground
28.
Max height = h; find max range
29.
A, B > 1; which magnitude of A×B is impossible
30.
What does not affect max height of projectile?
31.
If sum of two unit vectors is a unit vector, then magnitude of difference is?
32.
Range = 100 m. Where is KE maximum?
33.
Max height = 10 m. What’s max range?
34.
Particle in circular path, speed increases by g in 1 sec ⇒ net acceleration?
35.
Direction of motion from x-axis at instant?
36.
Elevation angle of projectile at highest point from origin
37.
Vector sum of two forces ⊥ to their difference ⇒ relation between forces
38.
Vector lies in plane of 𝑖̂ + 𝑗̂ and 𝑗̂ + 𝑘̂ and bisects angle between them
39.
Projectile at 45°, relation between Range R and Max Height H
40.
Direction cosines of î + ĵ + k̂
41.
x = 6t, y = 8t - 5t² ⇒ velocity of projection?
42.
Resultant of 2 vectors ⊥ to one, total = 18, resultant = 12 ⇒ find vectors
43.
Speed at highest point is √(2/5) of speed at half height ⇒ angle?
44.
Projectiles at 40° to horizontal (range = R₁) and 40° to vertical (range = R₂), then?
45.
Max speed over circular overbridge of radius R to avoid lifting
