The drawing shows a skateboarder moving at 5.71 m/s along a horizontal section of a track that is slanted upward by 49.8 ° above the horizontal at its end, which is 0.516 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track.
Vo = 5.71m/s[49.8o]
Yo = 5.71*sin49.8 = 4.36 m/s.
Y^2 = Yo^2 + 2g*h = 0 @ max. ht.
h = (Y^2-(Yo^2))/2g
h = (0-(4.36^2))/-19.6 = 0.970 m.
To find the maximum height H to which the skateboarder rises above the end of the track, we can use the principles of projectile motion and conservation of energy.
Step 1: Analyze the motion along the track
The skateboarder is moving at a constant velocity of 5.71 m/s along the horizontal section of the track. Since there is no vertical component of the velocity, we can ignore it in this stage of the motion.
Step 2: Determine the time taken to leave the track
To find the time taken for the skateboarder to leave the track, we need to analyze the vertical motion. When the skateboarder leaves the track, her initial vertical velocity is zero. The only force acting on her is gravity, causing her to fall vertically downward.
We can use the equation for vertical displacement in projectile motion:
h = v₀t + (1/2)gt²
Here, h is the vertical displacement, v₀ is the initial vertical velocity, t is the time taken, and g is the acceleration due to gravity.
Since h is given as 0.516 m and v₀ is 0, the equation becomes:
0.516 = (1/2)gt²
Solve this equation to find the time taken t to leave the track.
Step 3: Determine the maximum height
Once the skateboarder leaves the track, she follows a projectile path. At the highest point of this path, her vertical velocity is momentarily zero. Using this information, we can determine the maximum height H above the end of the track.
To find H, we can use the equation for vertical displacement in projectile motion:
H = v₀t + (1/2)gt²
Since v₀ is still 0, the equation becomes:
H = (1/2)gt²
Plug in the value of t we found in step 2 to calculate the maximum height H.
Step 4: Calculate the maximum height H
Plug the value of t into the equation for H:
H = (1/2)gt²
Using the value of g as 9.8 m/s² and the value of t found in step 2, solve for H to find the maximum height reached by the skateboarder.
Remember to consider significant figures and units while performing calculations and round your final answer appropriately.