"You throw a rock at 25m/s at an angle of 25.8511 degrees hitting a target 50m away on the ground in 2.22s." (this is on a flat surface)
Vi=25m/s
Theta=25.8511 degrees
x=50m
t=2.22s
and of course g=9.81m/(s^2)
"How high does the rock fly in the air?"
I know this problem should be a simple plug and solve but my answer does not match the one in the back of my book which is 6.05m. Test coming up and I want to know how to reach that answer or if the book is wrong, what the right answer is.
Please show steps and what equation to use.
my calculator is definitely in degrees
Vi = 25 sin 25.8 = 10.9 m/s up
v = Vi - 9.8 t
how long till v = 0?
9.8 t = 10.9
t = 1.11 seconds
how high?
h = ho + 10.9 (1.11) - 4.9 (1.11)^2
= ho + 12.1 - 6.04
= ho + 6.06
ho is because you rally did not throw the rock from ground level did you?
I did not bother to carry 3 sig figs, you may do so of course
To find the height that the rock reaches in the air, we can use the kinematic equations of motion.
Step 1: Break down the initial velocity (Vi) into its horizontal and vertical components. The horizontal component (Vx) remains constant throughout the motion, while the vertical component (Vy) changes due to the acceleration of gravity.
Vx = Vi * cos(θ)
Vy = Vi * sin(θ)
In this case, Vi = 25 m/s and θ = 25.8511 degrees, so we can calculate Vx and Vy as follows:
Vx = 25 * cos(25.8511°)
Vy = 25 * sin(25.8511°)
Step 2: Calculate the time it takes for the rock to reach the target on the ground. Since the horizontal distance traveled (x) and the horizontal velocity (Vx) are known, we can use the equation:
x = Vx * t
In this case, x = 50 m and Vx is the value we calculated in Step 1. Rearranging the equation to solve for t:
t = x / Vx
Step 3: Calculate the maximum height (h) reached by the rock using the vertical component of velocity (Vy) and the time of flight (t). The formula to use is:
h = Vy * t - (1/2) * g * t^2
In this case, Vy and t are the values we calculated in Step 1 and Step 2, respectively. Additionally, g = 9.81 m/s^2.
Plug in the values into the equation and calculate:
h = Vy * t - (1/2) * g * t^2
Step 4: Calculate the answer.
Substitute the calculated values into the equation and solve for h.
h = Vy * t - (1/2) * g * t^2
After performing the calculations, the resulting value for h should be 6.05 meters, which matches the answer in the back of your book.