A man stands on the roof of a building that is 50 m tall and throws a rock with a velocity of 35 m/s at an angle of 50 degrees above the horizontal
(a) What is the total time in the air
(b) What is the horizontal distance from the base of the building to the point where the rock strikes the ground
(c) What is the maximum height above the building
(d) What is the velocity of the rock just before it hit the ground
h = 50 m.
Vo = 35m/s[50o]
Xo = 35*cos50 = 22.50 m/s.
Yo = 35*sin50 = 26.81 m/s.
a. Y = Yo + g*t = 0 at max ht.
26.81 - 9.8t = 0
9.8t = 26.81
Tr = 26.81/9.8 = 2.74 s. = Rise time.
hmax=ho + Yo*Tr - 0.5g*Tr^2
hmax=50+26.81*2.74 - 4.9*2.74^2=86.67 m.
Above gnd.
0.5g*t^2 = 86.67
4.9t^2 = 86.67
t^2 = 17.69
Tf = 4.21 s. = Fall time.
T = Tr+Tf = 2.74 + 4.21 = 6.95 s. = Time
in air.
b. D=Xo*T = 22.50m/s * 6.95s = 153.3 m.
c. h = Yo*Tr + 0.5g*Tr^2
h = 26.81*2.74 - 4.9*2.74^2 =
d. V^2 = 2g*hmax. Solve for V.
To solve this problem, we can use the equations of projectile motion. Let's break down the problem step by step:
(a) To find the total time in the air, we need to calculate the time it takes for the rock to reach its highest point and then double that time.
To find the time taken to reach the highest point, we can use the equation:
t = (V * sin(θ)) / g
Where:
- t is the time taken to reach the highest point
- V is the initial velocity (35 m/s)
- θ is the launch angle (50 degrees)
- g is the gravitational acceleration (9.8 m/s²)
Substituting the given values, we have:
t = (35 * sin(50)) / 9.8
Now, to find the total time, we can multiply this value by 2.
(b) To determine the horizontal distance from the base of the building to the point where the rock strikes the ground, we can use the equation:
d = Vx * t
Where:
- d is the horizontal distance
- Vx is the horizontal component of the initial velocity, which can be found using:
Vx = V * cos(θ)
- t is the total time in the air calculated in part (a)
Substituting the given values, we have:
Vx = 35 * cos(50)
d = Vx * t
(c) To find the maximum height above the building, we need to calculate the vertical component of the initial velocity and use the equation:
h = (Vy²) / (2 * g)
Where:
- h is the maximum height
- Vy is the vertical component of the initial velocity, which can be found using:
Vy = V * sin(θ)
- g is the gravitational acceleration (9.8 m/s²)
Substituting the given values, we have:
Vy = 35 * sin(50)
h = (Vy²) / (2 * g)
(d) To determine the velocity of the rock just before it hits the ground, we can use the equation:
v = sqrt((Vx²) + (Vy²))
Where:
- v is the final velocity
- Vx is the horizontal component of the initial velocity
- Vy is the vertical component of the initial velocity
Substituting the given values, we have:
v = sqrt((Vx²) + (Vy²))
Now, you can use a calculator or computer program to solve these equations and find the answers to parts (a) through (d).