A motorcycle stuntman must jump from a ramp to a platform. The platform is located 15M away and is 2M higher then the tip of the ramp. The ramp is at a 35Degree angle. At what velocity must he travel as he leaves the ramp in order to reach the platform. Express in KM/h
v(x)=v• cosα, v(y) =v•sinα.
s=v(x) •t => t=s/v(x)=s/ v• cosα
h=v(y)•t-gt²/2=( v•sinα•s/v•cosα) – (g•s²/2•v²•cos²α).
Solve for “v, and obtain:
v=sqrt{g•s²/2cosα(s•sinα - h•cosα)=
13.82 m/s= 50 km/h
Im still confused on how you solved for V, would you mind plugging in the numbers for me? im completly lost
h=v(y)•t-gt²/2=( v•sinα•s/v•cosα) – (g•s²/2•v²•cos²α),
2•v²• cos²α•h=2•v²•s•sin α• cosα - g•s²,
g•s²=2•v²•s•sin α• cosα - 2•v²• cos²α•h,
g•s²= 2•v²• cosα(s•sin α-h•cosα).
v=sqrt{g•s²/2cosα(s•sinα - h•cosα)=
sqrt{9.8•15²/2•cos35(15•sin35-2•cos35)}=
13.82 m/s= 50 km/h
thanks!
To calculate the velocity required for the motorcycle stuntman to reach the platform, we can use the principles of projectile motion and the conservation of energy. Here are the steps to determine the answer:
Step 1: Identify the relevant variables:
- Distance to be covered horizontally (range): 15 meters
- Vertical displacement (height difference): 2 meters
- Angle of the ramp: 35 degrees
Step 2: Determine the initial vertical velocity (Vy):
Using the vertical displacement and the formula for vertical displacement in projectile motion:
Vy = √(2 * g * h)
where g is the acceleration due to gravity (9.8 m/s²) and h is the height difference.
Vy = √(2 * 9.8 * 2) = √(39.2) ≈ 6.26 m/s
Step 3: Determine the initial horizontal velocity (Vx):
Using the angle and the formula for horizontal velocity in projectile motion:
Vx = V * cos(θ)
where V is the initial velocity and θ is the angle of the ramp.
Step 4: Determine the initial velocity (V):
To calculate V, we can use the range formula in projectile motion:
Range = V * t
where t is the total time of flight. The time of flight can be determined using the vertical displacement and the vertical velocity:
t = 2 * Vy / g
Since the range is given as 15 meters, we can substitute the values into the formula and solve for V:
15 = V * (2 * Vy / g)
V * (2 * Vy / g) = 15
V = 15 / (2 * Vy / g)
V = 15 * g / (2 * Vy)
V = 15 * 9.8 / (2 * 6.26)
V ≈ 14.70 m/s
Step 5: Convert the velocity to km/h:
To convert the velocity from m/s to km/h, multiply it by 3.6:
V_kmh = V * 3.6
V_kmh ≈ 14.70 * 3.6
V_kmh ≈ 53 km/h
Therefore, the motorcycle stuntman must travel at approximately 53 km/h as he leaves the ramp to reach the platform.