Mid Term Review 1. A proton which is the nucleus of a hydrogen atom, can be mode
ID: 776928 • Letter: M
Question
Mid Term Review 1. A proton which is the nucleus of a hydrogen atom, can be modeled as a sphere, with a diameter of 2.4 x 101s m and mass of 1.67 x 10 kg. Determine the density of proton. 2. A ear is speeding down the road at 85 m/s. What is the speed in mi/h? 3. How many significant figures are in the quantity (a) 1230.0 m? 5 S (b)0.0053 kg? Planet A has eight times the radius of planet B. What is the ratio of their (a) Surface Areas (b) Volumes? A golf ball is released from rest at the top of a very tall building. Neglecting air resistance, calculate the position and velocity of the ball after 1,2 and 3 seconds. 4. 5. 6. A Bocing 777 aircraft takes off at 295 km/h after accelerating from rest at 2.80 m/s What is the minimum runway length required? 7. Consider two vectors A and B in the (x.y) plane. A = 3i + 4j-7kand B-i-2j +5k, where i and j are the vector units along the x and y axes. (a) Calculate the vectors C = 8A-15B and D 21 A + 50B (b) Calculate the magnitude of the vectors C and D A projectile is launched with an initial velocity of 60 m/s at an angle of 30° above the horizontal. The projectile lands on a hillside 4 seconds later. Neglect the air friction. (a) What is the projectile's velocity at the highest point of its trajectory? (b) What is the straight line distance from where the projeetile was launched to 8. where it hits the target? A baseball is thrown with a initial velocity of 40 m/s making an angle of 45° with the ground. Assume no air resistance and find: (a) The maximum height reached by the baseball. (b) The Horizontal Range 9.Explanation / Answer
There are many questions. So, I am solving the first four questions.
(1) Radius of the proton r = d/ 2 = (2.4 x 10^-15) / 2 = 1.2 x 10^-15 m
So, volume V = (4/3) x pi x r^3 = (4/3) x 3.141 x (1.2 x 10^-15)^3 = 7.24 x 10^-45 m^3
mass m = 1.67 x 10^-27 kg
So, density rho = m / V = (1.67 x 10^-27) / (7.24 x 10^-45) = 0.231 x 10^18 kg/m^3 = 2.31 x 10^17 kg/m^3
(2) Speed of the car v = 85 m/s
Convert this in km/h -
v = (85 x 60 x 60) / 1000 = 306 km/h
(3) (a) Three significant figures
(b) Two significant figures.
(4) Radius of planet A = r
so, radius of planet B = 8r
(a) Ratio of surface area = [4*pi*r^2] / [4*pi*(8r)^2] = 1 / 64
(b) Ratio of volumes = [(4/3)*pi*r^3] / [(4/3)*pi*(8r)^3] = 1 / 512