Final answer:
To find the initial velocity needed for the toy elf to jump over a 1.5 m high wall, we apply the Law of Conservation of Energy, setting kinetic energy equal to gravitational potential energy, which yields an initial velocity requirement of approximately 5.42 m/s.
Step-by-step explanation:
To solve for the initial velocity that the toy elf needs to jump over a 1.5 m high wall using the Law of Conservation of Energy, we start by equating the initial kinetic energy (KE) and the gravitational potential energy (PE) at the peak of the jump. The equation KE_initial + PE_initial = KE_final + PE_final simplifies to KE_initial = PE_final since the kinetic energy at the top is zero (the velocity is zero at the peak of the jump) and the potential energy at the initial point is also zero (the elf starts at ground level).
The formula for kinetic energy is KE = 1/2 mv^2, and for gravitational potential energy, the formula is PE = mgh, where m is mass, g is the acceleration due to gravity (9.81 m/s2), h is the height, and v is velocity. Setting 1/2 mv^2 = mgh and cancelling m from both sides gives 1/2 v^2 = gh. Substituting the height of 1.5 m gives us 1/2 v^2 = (9.81 m/s2)(1.5 m). Solving for v, we get v^2 = 2(9.81 m/s2)(1.5 m), so v = √(2 * 9.81 m/s2 * 1.5 m). After calculating, we find the initial velocity needs to be approximately 5.42 m/s.
In conclusion, the initial velocity for the toy elf to clear the wall is about 5.42 m/s. It's important to check the answer to make sure it's reasonable, for instance, that the velocity is not exceptionally high for a toy elf's jump.