German University in Cairo
Physics Department
PHYS 101 Winter 2025
Physics 101 Team
Sheet 1
A. Quantities, Units and Vectors
P1. A metallic alloy has mass of 1225 gram and has the shape of a cylinder that is
39.0 mm in height and 42.0 mm in diameter. What is the density of the alloy in SI
standard units? If this alloy is reformed into a solid sphere, calculate the radius of
this sphere and its surface area.
P2- A displacement vector that starts from the origin is given by 𝐴⃗ = 6𝑖̂ + 11𝑗̂ 𝑚.
Calculate the magnitude of this displacement and its direction by the angle with the
positive x-direction. Calculate also the unit vector in the direction of this displacement.
P3. A displacement vector that starts from the origin has a magnitude of 8.3 m and
makes an angle of 63o with the x-direction. Calculate the horizontal and vertical
components of this displacement, then write this displacement vector in unit vectors
notation. Calculate also the unit vector in the direction of this displacement.
P4. Consider the two displacement vectors
⃗⃗ = 12𝑖̂ − 7𝑗̂ 𝑚.
𝐴⃗ = 11𝑖̂ + 8𝑗̂ 𝑚 and 𝐵
⃗⃗, ( b) 𝐴⃗ − 𝐵
⃗⃗, (c) |𝐴⃗ − 𝐵
⃗⃗|
Calculate (a) 𝐴⃗ + 𝐵
⃗⃗| .
and (d) |𝐴⃗ + 𝐵
P5. Consider the two forces,
⃗⃗⃗⃗
𝐹1 = 12𝑖̂ + 8𝑗̂ + 7𝑘̂ N and ⃗⃗⃗⃗⃗
𝐹2 = 20𝑖̂ − 8𝑗̂ + 5𝑘̂ N .
Calculate the resultant force
𝐹⃗ = ⃗⃗⃗⃗
𝐹1 + ⃗⃗⃗⃗⃗
𝐹2 . Then calculate its magnitude.
Calculate also the unit vector in the direction of the resultant force.
P6. (Homework) Two spheres are cut from a certain uniform rock. One has radius 4.50
cm. The mass of the other is five times greater. Find the radius of the second one.
P7. (Homework) Assume it takes 7.00 min to fill a 30.0-liter gasoline tank. (a) Calculate
the rate at which the tank is filled in liter per second. (b) Calculate also the rate at
which the tank is filled in cubic meters per second.
P8. (Homework) A typical sugar cube has an edge length of 1 cm. If you had a cubical
box that contained 6.02 x1023 of sugar cubes, what would its edge length be?
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PHYS101 Winter 25
P9. Two vectors are given by
𝐴⃗ = 3𝑖̂ + 8𝑗̂ 𝑚
and
⃗⃗ = 12𝑖̂ − 5𝑗̂ 𝑚.
𝐵
Calculate the vector X that satisfies the vector equation
⃗⃑ = 0.
3𝐴⃑ + 2𝑋⃑ − 5𝐵
B. Motion
P1. A particle performs a displacement from the point ⃗⃗⃗⃗
𝑟1 = (21𝑖̂ + 8𝑗̂) 𝑚 to the
point ⃗⃗⃗⃗
𝑟2 = ( 111𝑖̂ + 89𝑗̂) 𝑚 during 9.0 seconds. Calculate its average velocity
vector (in unit vector notation) for this motion, calculate also the magnitude of this
velocity.
P2. A particle moves along the x-axis according to the equation x (t) = 10t 2, where
the position x is in meters and t is in seconds. Find the average velocity for the time
interval from 2.00 s to 4.00 s.
P2. A small metallic ball is thrown upward with speed 15 m/s from the top of a building
that is 25 m high above the ground. The ball passes vertically beside the wall of the
building while falling to the ground. Take the starting point as the origin, then calculate
the velocity and the position (displacement) of that ball at times t = 1, 2, 3 seconds
from the start of motion. Calculate also the time it needs to touch the ground.
P3. The height of an ascending helicopter above the ground is given by h =3.00t 3,
where h is in meters and t is in seconds. At t =2.00 s, the helicopter releases a small
solid ball. How long after its release will the ball reach the ground? Neglect air
resistance.
P4. Consider a particle that moves in the x-y plane. The instantaneous position of the
particle is given by
𝑟⃗(𝑡) = (5𝑡 3 + 4𝑡 2 )𝑖̂ + (7𝑡 2 − 1.2𝑡 4 )𝑗̂ 𝑚/𝑠.
Calculate:
1- The displacement between time t = 3.5 s and time t = 6.2 s.
2- The Average velocity corresponding to the displacement in 1.
3- The velocity of the particle at time t = 7.1 s.
4- The acceleration of the particle at t = 5.0 s.
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PHYS101 Winter 25