A stone propelled from a catapult with a speed of 59meter per seconds attain a height of 100 meter calculate
a. the time of flight
b. the angle of the projection
c. the range attain
I guess you mean maximum height of 100 m
Vertical problem:
Vi = 59 sin A
v = Vi - 9.81 t
at top v = 0
0 = Vi - 9.81 t
so
t = 59 sin A /9.81 at top
100 = Vi t - (9.81/2) t^2
100 = (59 sinA)^2/ 9.81 -(9.81/2) (59 sin a)^2/9.81^2
100 = (1/2)(59 sin A)^2/9.81
980*2 = (59 sin A)^2
44.27 = 59 sin A
A = 48.6 degrees
The rest is easy
sin A = .75
cos A = .661
time rising = 59 (.75)/9.81
= 4.51
SO TOTAL flight time = 2 t = 9.02 seconds (PART A)
angle A = 48.6 degrees (PART B)
range = 59 cos A * 9.02
= 352 meters (PART C)
time of flight t =2* 2hg =2*2*100/10 =2* 200/10 =2* 20 =2*4.47 =8.945
To solve this problem, we can use the equations of motion for projectile motion. Let's break down each part of your question:
a. The time of flight:
The time of flight is the total time it takes for the stone to go up to its maximum height and then return back to the ground. In projectile motion, the time of flight can be calculated using the formula:
Time of Flight = (2 * initial vertical velocity) / acceleration due to gravity
Given:
Initial vertical velocity (u) = 0 (as the stone starts from the ground)
Acceleration due to gravity (g) = -9.8 m/s^2 (considering downward direction as negative)
Using the formula, we can calculate the time of flight as follows:
Time of Flight = (2 * 59) / 9.8
b. The angle of the projection:
The angle of projection refers to the angle at which the stone is initially launched from the catapult. To determine this angle, we can use the equation for the vertical component of velocity:
Initial vertical velocity (u_y) = initial velocity * sin(angle)
Given:
Initial velocity (59 m/s) is provided.
To calculate the angle, we rearrange the equation:
Angle = arcsin(u_y / initial velocity)
Angle = arcsin (100 / 59)
c. The range attained:
The range is the horizontal distance covered by the stone. We can calculate it using the formula:
Range = (initial horizontal velocity * time of flight)
Given:
Initial horizontal velocity (u_x) = initial velocity * cos(angle)
Using the equation, we can calculate the range as follows:
Range = (59 * cos(angle)) * time of flight
Now you have all the steps to solve your problem. Plug in the values calculated in steps a and b to find the solution for step c.