a projectile is ejected from a 25 m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars. What is the ratio of the time taken to hit the ground on Mars compared to Earth? (Assume gravity on mars = .38gEarth)
The answer is 2.4
I keep getting 1.6 seconds. Please help me, with steps to solve if possible. I know its a long problem. Thank you so much in advance!
hf=hi+vi*t-1/2 g t^2
first, I am wondering is the 30 degrees above horizontal, or below horizonal. I will work it as ABOVE horizontal.
vi vertical= 40*sin30=20m/s
-25=0+20t-g/2 t^2
solve for t
t^2-40t/g -25-0
t= 20/g +- sqrt (400/g^2 + 25)
tearth=you do it.
tMars = you do it, g=.38*9.8
check my math.
That doesn't work out to the correct answer. I worked it the same as you but I get 1.4 instead of 2.4.
To solve this problem, we can use the laws of projectile motion. Let's break it down into steps:
Step 1: Find the time taken to hit the ground on Earth.
- We need to calculate the time of flight for the projectile on Earth. To do this, we can use the vertical motion equation:
h = ut + (1/2)gt^2
where h is the initial height of the tower (25 m), u is the initial vertical velocity (calculated as 40 m/s * sin(30)), g is the acceleration due to gravity on Earth (approximately 9.8 m/s^2), and t is the time of flight.
Substituting the values, we have:
25 = (40 * sin(30))t - (1/2) * 9.8 * t^2
Simplifying:
25 = 20t - 4.9t^2
Rearranging the equation to a quadratic form:
4.9t^2 - 20t + 25 = 0
By solving this quadratic equation, you will get two possible solutions for t. Select the positive value since time cannot be negative.
Step 2: Find the time taken to hit the ground on Mars.
- We need to calculate the time of flight for the projectile on Mars. Since the gravity on Mars is given as 0.38 times the gravity on Earth, we can use the same vertical motion equation:
25 = (40 * sin(30))t - (1/2) * (0.38 * 9.8) * t^2
Simplifying:
25 = 20t - 1.86t^2
Rearranging the equation to a quadratic form:
1.86t^2 - 20t + 25 = 0
By solving this quadratic equation, you will get two possible solutions for t. Select the positive value since time cannot be negative.
Step 3: Calculate the ratio of the time taken to hit the ground on Mars compared to Earth.
- Divide the time taken to hit the ground on Mars by the time taken to hit the ground on Earth:
Ratio = (time on Mars) / (time on Earth)
So, to get the final answer, plug in the calculated times from Step 1 and Step 2 into the ratio equation.
If you're getting a different answer, double-check your calculations and make sure you're using the correct values for gravity on Earth and Mars.