A rider with his bike, weighing a total of 300 kg jumps off a sloped ramp with a speed of 5.5 m/s. How high will the biker jump with this speed?
At what speed should a ball of mass 2 kg be rolled in order to reach the other side of a 6 m high slope?
1.50 m
A woman wearing high-heeled shoes stands on a wooden floor. Her total weight is 480N and acts equally on each foot.
Sometimes all this weight acts on the heels of her shoes. What is the pressure under her heels?
Well, if the biker jumps off a sloped ramp with a speed of 5.5 m/s, I'm not sure about the exact height he'll reach, but I can tell you this - he'll definitely be reaching new heights both literally and metaphorically! It's like flying through the air with the greatest of ease, except on a bike, so maybe we can call it "bike flying"? Anyway, gravity might have a say in this, but I doubt it can dampen the biker's excitement. Safe travels, my two-wheeled friend!
To determine how high the biker will jump with a speed of 5.5 m/s, we can use the principle of conservation of mechanical energy. This principle states that the total mechanical energy of the system, which includes the potential energy and the kinetic energy, remains constant as long as no external forces are acting on the system.
The total mechanical energy can be expressed as the sum of the gravitational potential energy and the kinetic energy:
Total Mechanical Energy = Potential Energy + Kinetic Energy
The potential energy is given by the equation:
Potential Energy = m * g * h
where m is the mass of the system (rider + bike) in kg, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height in meters.
The kinetic energy is given by the equation:
Kinetic Energy = (1/2) * m * v^2
where v is the speed in m/s.
Since the total mechanical energy remains constant, we can equate the initial potential energy and kinetic energy to the final potential energy when the biker reaches the highest point of the jump:
m * g * h_initial + (1/2) * m * v^2 = m * g * h_final
We can cancel out the mass (m) from both sides of the equation, which gives us:
g * h_initial + (1/2) * v^2 = g * h_final
Rearranging the equation to solve for h_final:
h_final = (g * h_initial) + (1/2) * v^2 / g
Now, let's plug in the values:
h_initial = 0 (assuming the biker starts at ground level)
v = 5.5 m/s
g = 9.8 m/s^2
h_final = (9.8 * 0) + (1/2) * (5.5^2) / 9.8
Simplifying the equation:
h_final = 0 + (1/2) * 30.25 / 9.8
h_final = (1/2) * 3.0878
h_final = 1.5439 meters
Therefore, the biker will jump approximately 1.54 meters high with a speed of 5.5 m/s.