While Hiking in the wilderness, you come to the top of a cliff that is 60.0m high. you throw a stone from the cliff, giving it an initial velocity of 21m/s at 35deg above the horizontal. How far from the base of the cliff does the stone land? (85m)
I tried this question but i get the answer as 75m. I found the time and there after the horizontal component and multiplied it together. Please help.
You did it correctly, let me see your calculations.
actually I got the same answer as yours and I did the same thing so the book is wrong probably
Full work has been shown at #2 here:
aquantaday.wordpress.com/grade-12-physics-challenge-problems-1-kinematics/
The answer is indeed 85 m.
Sure! I'd be happy to help you with this question.
To find the distance from the base of the cliff where the stone lands, we first need to break down the motion of the stone into its horizontal and vertical components.
Let's start by finding the time it takes for the stone to hit the ground. We can use the vertical motion equation:
h = ut + (1/2)gt^2
Where:
h = height (initially 60.0m)
u = initial vertical velocity (in this case, the vertical component of the initial velocity is 21m/s * sin(35))
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Plugging in the values, we have:
60.0m = (21m/s * sin(35))t - (1/2)(9.8m/s^2)t^2
Simplifying the equation yields a quadratic equation in terms of t:
4.9t^2 - 0.5736t - 10.0 = 0
Solving this quadratic equation will give us the time it takes for the stone to hit the ground.
Using the quadratic formula:
t = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 4.9, b = -0.5736, and c = -10.0. Plugging these values into the quadratic formula, we can solve for t.
After finding the time, we can use the horizontal motion of the stone to find the distance it travels. The horizontal component of the initial velocity is given by 21m/s * cos(35).
The formula to find the horizontal distance is:
d = ut
Where:
d = distance
u = initial horizontal velocity (in this case, the horizontal component of the initial velocity is 21m/s * cos(35))
t = time
Plugging in the values, we have:
d = (21m/s * cos(35)) * t
Using the value of t obtained earlier, we can calculate the distance d.
By following these steps, you should be able to find the correct distance from the base of the cliff where the stone lands.